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D.3 Motion in electromagnetic fields

Practice exam-style IB Physics questions for Motion in electromagnetic fields, aligned with the syllabus and grouped by topic.

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Question 1
SL • Paper 1A
Easy
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SL • Paper 1A
Easy
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A particle of charge +2.0×10−6 C+2.0\times 10^{-6}\ \text{C} and mass 4.0×10−9 kg4.0\times 10^{-9}\ \text{kg} is in a uniform electric field of strength 3.0×104 N C−13.0\times 10^4\ \text{N C}^{-1}.

What is the magnitude of the acceleration of the particle?

A.

2.4×108 m s−22.4\times 10^8\ \text{m s}^{-2}

B.

7.5×10−8 m s−27.5\times 10^{-8}\ \text{m s}^{-2}

C.

1.5×107 m s−21.5\times 10^7\ \text{m s}^{-2}

D.

6.0×10−2 m s−26.0\times 10^{-2}\ \text{m s}^{-2}

Question 2
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A charged particle moves perpendicular to a uniform magnetic field and remains within the field.

What is correct about the speed and kinetic energy of the particle while it is in the magnetic field?

A.

The speed increases but the kinetic energy remains constant.

B.

The speed remains constant but the kinetic energy increases.

C.

Both speed and kinetic energy increase.

D.

Both speed and kinetic energy remain constant.

Question 3
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A positive ion enters the region between two parallel plates with a horizontal velocity. The uniform electric field between the plates is vertically downwards. The ion enters midway between the plates.

Which path is followed by the ion while it is between the plates?

A.
A small option diagram showing two parallel horizontal plates, a positive ion entering from the left midway between them with a horizontal velocity arrow, and a straight horizontal track through the centre of the plates. The electric field direction is indicated by several downward arrows between the plates.
B.
A small option diagram showing two parallel horizontal plates, a positive ion entering from the left midway between them with a horizontal velocity arrow, and a smooth parabolic track curving downward as it travels to the right. The electric field direction is indicated by several downward arrows between the plates.
C.
A small option diagram showing two parallel horizontal plates, a positive ion entering from the left midway between them with a horizontal velocity arrow, and a smooth parabolic track curving upward as it travels to the right. The electric field direction is indicated by several downward arrows between the plates.
D.
A small option diagram showing two parallel horizontal plates, a positive ion entering from the left midway between them with a horizontal velocity arrow, and a circular arc bending downward as it travels to the right. The electric field direction is indicated by several downward arrows between the plates.
Question 4
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
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A long straight vertical wire carries a conventional current upwards.

Which diagram shows the direction of the magnetic field around the wire when viewed from above?

A.
A top-view option diagram showing a small central circle representing the wire with a dot or upward-current label at the centre. Several concentric circular magnetic field lines surround the wire with arrowheads indicating an anticlockwise direction. The diagram is clean black line art on a white background.
B.
A top-view option diagram showing a small central circle representing the wire with a dot or upward-current label at the centre. Several straight magnetic field lines point radially inward toward the wire. The diagram is clean black line art on a white background.
C.
A top-view option diagram showing a small central circle representing the wire with a dot or upward-current label at the centre. Several concentric circular magnetic field lines surround the wire with arrowheads indicating a clockwise direction. The diagram is clean black line art on a white background.
D.
A top-view option diagram showing a small central circle representing the wire with a dot or upward-current label at the centre. Several straight magnetic field lines radiate outward from the wire with arrowheads pointing away from the centre. The diagram is clean black line art on a white background.

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Question 5
SL • Paper 2
Easy
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SL • Paper 2
Easy
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An alpha particle of charge +3.20×10−19 C+3.20\times10^{-19}\ \text{C} moves at 1.5×106 m s−11.5\times10^{6}\ \text{m s}^{-1} in a uniform magnetic field of flux density 0.40 T0.40\ \text{T}. The angle between the velocity of the alpha particle and the magnetic field is 30∘30^\circ.

A

Determine the magnitude of the magnetic force on the alpha particle.

[2]
B

State why the component of velocity parallel to the magnetic field is unchanged.

[1]
Question 6
SL • Paper 2
Easy
Calculator Permitted
SL • Paper 2
Easy
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A straight wire of length 6.0 cm6.0\ \text{cm} is placed at right angles to a uniform magnetic field of flux density 0.18 T0.18\ \text{T}. The current in the wire is 3.5 A3.5\ \text{A}.

Apparatus-style diagram showing a straight horizontal wire between the poles of a magnet. The magnetic field is uniform and perpendicular to the wire. The current direction is indicated, but the force direction is not shown.
A

Determine the magnetic force on the wire.

[2]
B

State the effect on the force if the direction of the current is reversed.

[1]
Question 7
SL • Paper 1A
Medium
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SL • Paper 1A
Medium
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A beam of singly charged ions passes undeflected through perpendicular uniform electric and magnetic fields. The electric field strength is 4.8×104 V m−14.8\times10^4\ \text{V m}^{-1} and the magnetic field strength is 0.16 T0.16\ \text{T}.

What is the speed of the ions?

A.

7.7×103 m s−17.7\times10^3\ \text{m s}^{-1}

B.

7.7×106 m s−17.7\times10^6\ \text{m s}^{-1}

C.

3.0×105 m s−13.0\times10^5\ \text{m s}^{-1}

D.

1.3×106 m s−11.3\times10^6\ \text{m s}^{-1}

Question 8
SL • Paper 1A
Medium
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SL • Paper 1A
Medium
Calculator Permitted

A particle with charge magnitude 3.2×10−19 C3.2\times10^{-19}\ \text{C} moves at 5.0×106 m s−15.0\times10^6\ \text{m s}^{-1} in a uniform magnetic field of flux density 0.20 T0.20\ \text{T}. The angle between the velocity and the magnetic field is 30∘30^\circ.

What is the magnitude of the magnetic force on the particle?

A.

1.6×10−13 N1.6\times10^{-13}\ \text{N}

B.

5.5×10−13 N5.5\times10^{-13}\ \text{N}

C.

3.2×10−13 N3.2\times10^{-13}\ \text{N}

D.

8.0×10−26 N8.0\times10^{-26}\ \text{N}

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Question 9
SL • Paper 1A
Medium
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SL • Paper 1A
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Two long parallel wires carry currents in opposite directions. The currents are then both doubled and the separation of the wires is also doubled.

What happens to the force per unit length between the wires?

A.

It remains repulsive and has the same magnitude.

B.

It becomes attractive and doubles in magnitude.

C.

It remains repulsive and doubles in magnitude.

D.

It becomes attractive and is halved in magnitude.

Question 10
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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A charged particle enters a uniform magnetic field with velocity at an angle between 0∘0^\circ and 90∘90^\circ to the magnetic field direction.

What is the resulting path of the particle?

A.

A straight line parallel to the field

B.

A circle in a plane perpendicular to the field

C.

A helix with its axis parallel to the field

D.

A parabola in a plane containing the field

Question 11
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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A straight horizontal wire carries conventional current to the right. The wire is in a uniform magnetic field directed into the plane of the page.

What is the direction of the magnetic force on the wire?

A simple diagram showing a straight horizontal wire across the centre of the page with an arrow on the wire pointing to the right labelled current. The surrounding uniform magnetic field is represented by evenly spaced crosses, indicating a field into the page. No force arrow is shown.
A.

Downwards

B.

Into the plane of the page

C.

Upwards

D.

Out of the plane of the page

Question 12
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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In a mass spectrometer, positive ions pass through a velocity selector and then enter a region containing only a uniform magnetic field. The ions all have the same charge and pass through the selector with the same speed.

What is correct for ions of greater mass in the magnetic-field region?

A.

They are not deflected because the velocity selector has balanced the forces.

B.

They follow the same radius because their speed is the same.

C.

They follow a path of larger radius because their mass-to-charge ratio is larger.

D.

They follow a path of smaller radius because their charge-to-mass ratio is smaller.

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Question 13
SL • Paper 2
Medium
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SL • Paper 2
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An electron enters the uniform electric field between two horizontal parallel plates with an initial horizontal velocity. The upper plate is positive and the lower plate is negative. The potential difference between the plates is 480 V480\ \text{V} and their separation is 24 mm24\ \text{mm}.

Side-view diagram of two horizontal parallel plates with the upper plate labelled positive and the lower plate labelled negative. An electron enters midway between the plates from the left with a horizontal velocity arrow. Uniform electric field lines are shown between the plates, but no trajectory is drawn.
A

Determine the magnitude of the electric field strength between the plates.

[1]
B

State the direction of the acceleration of the electron while it is between the plates.

[1]
C

Explain why the path of the electron is parabolic while it is between the plates.

[2]
Question 14
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
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A proton of speed 2.4×106 m s−12.4 \times 10^{6}\ \text{m s}^{-1} enters a region of uniform magnetic field of flux density 0.32 T0.32\ \text{T}. The velocity of the proton is perpendicular to the magnetic field, which is directed into the page.

Diagram showing a proton entering a rectangular region containing uniformly spaced cross symbols representing a magnetic field into the page. The proton has a velocity arrow perpendicular to the field. No circular path or centre of curvature is shown.
A

State the direction of the magnetic force on the proton at the instant it enters the field.

[1]
B

Determine the radius of the circular path of the proton.

[2]
C

Explain why the kinetic energy of the proton remains constant in the magnetic field.

[1]
Question 15
SL • Paper 2
Medium
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SL • Paper 2
Medium
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Positive ions pass through a velocity selector. The ions move horizontally to the right through a uniform electric field of strength 6.0×104 V m−16.0\times10^{4}\ \text{V m}^{-1} directed upwards and a uniform magnetic field of flux density 0.20 T0.20\ \text{T} directed out of the page.

Diagram of a velocity selector with positive ions travelling horizontally between plates. Electric field arrows point upward and magnetic field dots indicate a field out of the page. The ion beam is shown entering but no deflected paths are shown.
A

Determine the speed of ions that pass through undeflected.

[2]
B

State the initial direction of deflection of a positive ion that enters with a smaller speed.

[1]
Question 16
SL • Paper 2
Medium
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SL • Paper 2
Medium
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Two long parallel wires are separated by 4.0 cm4.0\ \text{cm}. The currents in the wires are 12 A12\ \text{A} and 8.0 A8.0\ \text{A} in the same direction.

End-on or perspective diagram of two long, straight, parallel wires separated by a labelled distance. Arrows on both wires show currents in the same direction. No force arrows are shown.
A

Determine the force per unit length on either wire.

[2]
B

State whether the force is attractive or repulsive.

[1]

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Question 17
HL • Paper 2
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HL • Paper 2
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A proton is accelerated from rest through a potential difference of 2.00 kV2.00\ \text{kV} in a vacuum. After acceleration it enters a second uniform electric field directed opposite to its velocity.

A

Determine the speed of the proton after it has been accelerated through the potential difference.

[3]
B

Explain why the proton slows down in the second electric field.

[1]
Question 18
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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Electrons enter a uniform electric field between two horizontal parallel plates with initial horizontal speed 3.0×106 m s−13.0 \times 10^6\ \text{m s}^{-1}. The vertical deflection sys_y is measured for different lengths XX of the field region. The initial vertical velocity of the electrons is zero.

Vertical deflection of an electron beam plotted against X².
A

Describe what the graph shows about the relationship between sys_y and XX.

[1]
B

Use the graph to determine the vertical acceleration of the electrons in the field.

[2]
C

The polarity of the plates is reversed while the magnitude of the potential difference is unchanged. Explain the effect on the electron beam.

[1]
Question 19
SL • Paper 1B
Medium
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SL • Paper 1B
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A proton enters a region of uniform magnetic field at point P. The magnetic field is directed into the plane of the page. The proton follows the circular path shown.

An annotated plan-view diagram of a proton track in a uniform magnetic field represented by crosses. The proton enters from the left at point P with its initial velocity horizontally to the right and curves upward in a circular arc. A scale or radius marker is included so that the radius of curvature of the path can be determined. The magnetic field strength is labelled as $0.45\ \text{T}$.
A

State the direction of the magnetic force on the proton at P.

[1]
B

Determine the speed of the proton. Use mp=1.67×10−27 kgm_p = 1.67 \times 10^{-27}\ \text{kg} and qp=1.60×10−19 Cq_p = 1.60 \times 10^{-19}\ \text{C}.

[2]
C

Explain why the kinetic energy of the proton remains constant while it is in the magnetic field.

[1]
Question 20
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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A beam of singly charged positive ions passes through perpendicular uniform electric and magnetic fields. The electric field strength is 7.2×104 V m−17.2 \times 10^4\ \text{V m}^{-1}. The vertical deflection of the beam is recorded for different ion speeds.

Ion speed / m s−1^{-1}

Vertical deflection / mm

1.8×1051.8 \times 10^{5}

+4.8

2.1×1052.1 \times 10^{5}

+2.4

2.4×1052.4 \times 10^{5}

0.0

2.7×1052.7 \times 10^{5}

-2.4

3.0×1053.0 \times 10^{5}

-4.8

A

Determine the speed of the ions that pass through undeflected.

[1]
B

Calculate the magnetic field strength in the selector.

[2]
C

Explain why the selected speed is independent of the charge and mass of the ions.

[1]

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Question 21
HL • Paper 1A
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HL • Paper 1A
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Electrons are accelerated from rest through a potential difference VV and then enter a uniform magnetic field of flux density BB at right angles. The radius of their circular path is rr.

What expression gives the specific charge e/me/m of the electron?

A.

B2r22V\dfrac{B^2r^2}{2V}

B.

2VBr2\dfrac{2VB}{r^2}

C.

Vr2B2\dfrac{Vr}{2B^2}

D.

2VB2r2\dfrac{2V}{B^2r^2}

Question 22
HL • Paper 1A
Medium
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HL • Paper 1A
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Two long parallel wires are separated by 0.050 m0.050\ \text{m}. They carry currents of 4.0 A4.0\ \text{A} and 6.0 A6.0\ \text{A} in the same direction.

What is the force per unit length between the wires? Use μ0=4π×10−7 N A−2\mu_0=4\pi\times10^{-7}\ \text{N A}^{-2}.

A.

9.6×10−5 N m−19.6\times10^{-5}\ \text{N m}^{-1}, attractive

B.

1.9×10−4 N m−11.9\times10^{-4}\ \text{N m}^{-1}, repulsive

C.

9.6×10−5 N m−19.6\times10^{-5}\ \text{N m}^{-1}, repulsive

D.

4.8×10−5 N m−14.8\times10^{-5}\ \text{N m}^{-1}, attractive

Question 23
HL • Paper 2
Medium
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HL • Paper 2
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Electrons are accelerated from rest through a potential difference VV and then enter a uniform magnetic field at right angles to the field. The path in the magnetic field is circular. In one experiment, V=250 VV=250\ \text{V}, B=3.0 mTB=3.0\ \text{mT} and the radius of the path is 18 mm18\ \text{mm}.

Fine-beam tube style diagram showing an electron beam accelerated between plates and then entering a uniform magnetic field perpendicular to the beam. A visible circular track is shown with its radius labelled symbolically, but no numerical values are embedded in the diagram.
A

Show that the specific charge of the electron is given by qm=2VB2r2\frac{q}{m}=\frac{2V}{B^2r^2}.

[2]
B

Determine the specific charge of the electron from the experimental data.

[2]
Question 24
HL • Paper 2
Medium
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HL • Paper 2
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A singly charged positive ion of mass 6.64×10−27 kg6.64\times10^{-27}\ \text{kg} enters a uniform magnetic field of flux density 0.12 T0.12\ \text{T} with speed 4.0×105 m s−14.0\times10^{5}\ \text{m s}^{-1}. The velocity of the ion makes an angle of 35∘35^\circ with the direction of the magnetic field.

Three-dimensional schematic showing a uniform magnetic field represented by parallel arrows. A positive ion enters with a velocity arrow at an angle to the field. A helical path is suggested qualitatively but without radius or pitch values.
A

Explain why the subsequent path of the ion is a helix.

[2]
B

Determine the radius of the helical path.

[2]

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Question 25
HL • Paper 2
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HL • Paper 2
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In a mass spectrometer, singly charged positive ions first pass undeflected through a velocity selector. The electric field in the selector is 1.8×105 V m−11.8\times10^{5}\ \text{V m}^{-1} and the magnetic field is 0.30 T0.30\ \text{T}. The ions then enter a second region containing only a uniform magnetic field of flux density 0.50 T0.50\ \text{T}, where their circular path has radius 0.125 m0.125\ \text{m}.

Schematic of a Bainbridge-type mass spectrometer. In the velocity selector, positive ions move right through crossed fields with the electric field upward and the magnetic field out of the page so that the forces cancel and the beam remains straight. The ions then enter a magnetic-field-only region where they curve toward a detector. The diagram labels the two regions symbolically but does not include numerical values or the final answer.
A

Determine the speed selected by the velocity selector.

[1]
B

Determine the mass of the ion.

[2]
C

State how the radius would change for a heavier isotope with the same charge and the same selected speed.

[1]
Question 26
HL • Paper 2
Medium
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HL • Paper 2
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In an investigation of the force on a current-carrying conductor, a straight wire of length 0.080 m0.080\ \text{m} is held perpendicular to a uniform magnetic field. The force on the wire is measured for different currents. The best-fit gradient of the graph of force against current is 2.40×10−3 N A−12.40\times10^{-3}\ \text{N A}^{-1}.

Measured force on a straight wire for different currents.
A

Determine the magnetic flux density of the field.

[2]
B

Explain why a straight line through the origin supports the model F=BILsin⁡θF=BIL\sin\theta for this investigation.

[2]
Question 27
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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A straight horizontal wire of length 5.0 cm5.0\ \text{cm} is placed at right angles to a uniform magnetic field. The wire is connected to a variable current supply and the magnetic force on the wire is measured using a balance.

Magnetic force on a wire plotted against current.
A

Use the graph to determine the magnetic field strength.

[2]
B

Predict the magnitude of the magnetic force when the current is 3.5 A3.5\ \text{A}.

[1]
C

Suggest one advantage of taking readings for both directions of current.

[1]
Question 28
SL • Paper 1B
Medium
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SL • Paper 1B
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Two long parallel wires carry equal currents in the same direction. The force per unit length on one wire is measured for different separations rr.

Force per unit length against reciprocal separation.
A

State the relationship between the force per unit length and the separation of the wires.

[1]
B

Use the graph to determine the current in each wire. Use μ0=4π×10−7 N A−2\mu_0 = 4\pi \times 10^{-7}\ \text{N A}^{-2}.

[2]
C

State the direction of the force between the wires.

[1]

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Question 29
SL • Paper 1B
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SL • Paper 1B
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Positive ions of speed 4.0×105 m s−14.0 \times 10^5\ \text{m s}^{-1} move through a uniform magnetic field of strength 0.25 T0.25\ \text{T}. The angle θ\theta between the ion velocity and the magnetic field is varied.

Magnetic force on a positive ion plotted against sin θ.
A

Explain why plotting the force against sin⁡θ\sin\theta gives a straight line.

[1]
B

Use the graph to determine the charge of the ion.

[2]
C

State the force on the ion when it moves parallel to the magnetic field.

[1]
Question 30
HL • Paper 2
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HL • Paper 2
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Two long vertical wires are separated by 25 mm25\ \text{mm}. Each wire carries a current of 15 A15\ \text{A} upwards. At the location of the experiment, the horizontal component of Earth's magnetic field is 50 μT50\ \mu\text{T}.

Diagram of two long parallel vertical wires separated by a small distance. Both current arrows point upwards. A horizontal Earth-field arrow is also shown, but no resultant force arrows are included.
A

Determine the magnetic field strength produced by one wire at the position of the other wire.

[2]
B

Explain whether the force between the wires is attractive or repulsive.

[1]
C

Compare the field due to one wire with Earth's horizontal magnetic field and comment on whether Earth's field can be ignored in a precise experiment.

[1]
Question 31
HL • Paper 1B
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HL • Paper 1B
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Electrons are accelerated from rest through a potential difference VV and then enter a uniform magnetic field of strength 1.50 mT1.50\ \text{mT} at right angles. Their circular path radius rr is measured in a fine-beam tube.

Accelerating potential difference plotted against radius squared for electrons in a fine-beam tube.
A

State why a graph of VV against r2r^2 is expected to be linear.

[1]
B

Use the graph to determine the electron charge-to-mass ratio em\frac{e}{m}.

[2]
C

Compare the value obtained with the accepted value 1.76×1011 C kg−11.76 \times 10^{11}\ \text{C kg}^{-1}.

[1]
D

Suggest why the lowest-radius points have the largest fractional uncertainty.

[1]
Question 32
HL • Paper 1B
Hard
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HL • Paper 1B
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A mass spectrometer uses a velocity selector followed by a region containing only a uniform magnetic field. Singly charged positive ions pass undeflected through the selector and then strike a detector at two positions, A and B. The electric field in the selector is 2.40×104 V m−12.40 \times 10^4\ \text{V m}^{-1} and the magnetic field in the selector is 0.120 T0.120\ \text{T}. The magnetic field in the analyser region is 0.150 T0.150\ \text{T}.

An annotated schematic of a Bainbridge-type mass spectrometer. It shows a crossed-field velocity selector followed by a magnetic-field-only analyser region with two semicircular ion paths ending at detector positions labelled A and B. The radii of the two paths can be read from a scale, with path B having the larger radius. Field-direction arrows are omitted.
A

Calculate the speed of ions transmitted by the velocity selector.

[1]
B

Determine the mass of the ion that reaches detector position A. Use e=1.60×10−19 Ce = 1.60 \times 10^{-19}\ \text{C}.

[2]
C

Use the detector positions to determine the ratio mBmA\frac{m_B}{m_A}.

[1]
D

Explain why the ion reaching B has the larger mass.

[1]

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Question 33
HL • Paper 1B
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HL • Paper 1B
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Alpha particles enter a uniform magnetic field at an angle to the field direction and follow a helical path. The magnetic field strength is 0.50 T0.50\ \text{T}. For an alpha particle, q=3.20×10−19 Cq = 3.20 \times 10^{-19}\ \text{C} and m=6.64×10−27 kgm = 6.64 \times 10^{-27}\ \text{kg}.

A three-dimensional annotated diagram of a helical alpha-particle path around a straight magnetic field direction. The field direction is shown by parallel arrows. The helix radius and pitch are marked with dimension arrows and a scale, allowing both quantities to be determined. The radius is visibly much smaller than the pitch.
A

Use the radius of the helix to determine the component of the alpha-particle velocity perpendicular to the magnetic field.

[2]
B

Calculate the time for one complete turn of the helix.

[1]
C

Use the pitch of the helix to determine the component of velocity parallel to the magnetic field.

[1]
D

Explain why the path is helical rather than circular.

[1]
Question 34
HL • Paper 1B
Hard
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HL • Paper 1B
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In a velocity-selector experiment, the magnetic field in the selector is fixed at 0.080 T0.080\ \text{T} while the electric field strength is varied. The ions then enter an analyser region where a magnetic field of strength 0.200 T0.200\ \text{T} bends the transmitted beam to a detector.

Electric field / 10410^4 V m−1^{-1}

Detector current / a.u.

Analyser radius / m

2.60

0.07

0.260

2.80

0.22

0.260

3.00

0.54

0.260

3.10

0.81

0.260

3.20

1.00

0.260

3.30

0.79

0.260

3.40

0.53

0.260

3.60

0.21

0.260

3.80

0.08

0.260

A

Determine the electric field strength at which the transmitted ion current is maximum.

[1]
B

Calculate the speed of the ions at maximum transmitted current.

[1]
C

Use the analyser path to determine the mass-to-charge ratio of the ions.

[2]
D

Suggest why the current peak has a finite width rather than occurring at a single value of electric field strength.

[1]
Question 35
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

An electron enters midway between two horizontal parallel metal plates with horizontal speed 2.4×107 m s−12.4\times 10^7\ \text{m s}^{-1}. The potential difference between the plates is 420 V420\ \text{V} and their separation is 4.0 cm4.0\ \text{cm}. The uniform-field region has length 8.0 cm8.0\ \text{cm}. The upper plate is positive.

Side-view diagram of two horizontal parallel plates with the upper plate labelled positive and the lower plate labelled negative. An electron enters midway between the plates from the left with a horizontal velocity arrow. The length of the field region and the plate separation are labelled. The diagram should show the plates but not the electron trajectory.
A
I.

Determine the magnitude of the electric field strength between the plates.

[1]
II.

Calculate the acceleration of the electron while it is between the plates.

[2]
B

Show that the electron does not strike a plate before leaving the field region.

[2]
C

Explain how the path would change if the electron entered with the same speed but the potential difference was reversed.

[2]
Question 36
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A proton enters a uniform magnetic field of flux density 0.12 T0.12\ \text{T} with speed 3.0×106 m s−13.0\times 10^6\ \text{m s}^{-1}. The velocity is perpendicular to the field, which is directed out of the plane of the page.

Top-view diagram of a rectangular region filled with repeated dot symbols indicating a uniform magnetic field out of the page. A proton enters the region from the left with a rightward velocity arrow. No path or force arrow is shown.
A
I.

State the initial direction of the magnetic force on the proton.

[1]
II.

Explain why the proton follows a circular path while it remains in the field.

[2]
B

Calculate the radius of the circular path.

[2]
C

Evaluate the statement: “The proton is accelerating in the magnetic field, so its kinetic energy increases.”

[2]

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Question 37
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A straight wire of length 5.5 cm5.5\ \text{cm} is placed at right angles to a uniform magnetic field of flux density 0.35 T0.35\ \text{T}. The wire is connected to a power supply and rests between the poles of a magnet on a sensitive balance. The current in the wire is 4.2 A4.2\ \text{A}.

Apparatus diagram showing a straight horizontal wire segment between the poles of a magnet on a balance. No magnetic-field or current-direction arrows are shown. The balance display is shown without a numerical reading.
A
I.

Calculate the magnitude of the magnetic force on the wire.

[2]
II.

State one change that would reverse the direction of this force.

[1]
B

Explain why the balance reading changes when the current is switched on.

[2]
C

Evaluate why measurements are often taken for both current directions when determining BB using this apparatus.

[2]
Question 38
HL • Paper 1B
Hard
Calculator Permitted
HL • Paper 1B
Hard
Calculator Permitted

Two long straight parallel wires are separated by a fixed centre-to-centre distance of 4.0 cm4.0\ \text{cm}. The currents are varied and the force per unit length is measured. The product of the currents is I1I2I_1I_2.

Force per unit length against I1I2 for two parallel wires.
A

Describe the evidence from the graph that the force per unit length is proportional to I1I2I_1I_2.

[1]
B

Use the graph to determine an experimental value for μ0\mu_0.

[2]
C

Calculate the percentage difference between this value and 4π×10−7 N A−24\pi \times 10^{-7}\ \text{N A}^{-2}.

[1]
D

The separation is accidentally measured between the nearest surfaces of the wires rather than between their centres. State the effect on the calculated value of μ0\mu_0.

[1]
Question 39
HL • Paper 1B
Hard
Calculator Permitted
HL • Paper 1B
Hard
Calculator Permitted

An electron travels parallel to a long straight wire carrying a steady conventional current of 60 A60\ \text{A} upwards. At the instant shown, the electron is 2.0 cm2.0\ \text{cm} to the right of the wire and has speed 3.0×106 m s−13.0 \times 10^6\ \text{m s}^{-1} upwards. Use e=1.60×10−19 Ce = 1.60 \times 10^{-19}\ \text{C} and μ0=4π×10−7 N A−2\mu_0 = 4\pi \times 10^{-7}\ \text{N A}^{-2}.

An annotated diagram of a vertical long straight wire with conventional current upward. An electron is shown to the right of the wire with a velocity arrow upward, parallel to the wire. The perpendicular distance from the wire to the electron is labelled. The diagram includes a small right-hand grip rule inset indicating the circular magnetic field around the wire, but not the force direction on the electron.
A

Calculate the magnetic field strength at the position of the electron due to the wire.

[2]
B

Calculate the magnitude of the magnetic force on the electron at this instant.

[1]
C

Determine the direction of the magnetic force on the electron.

[1]
D

Explain why the subsequent path of the electron is not a circular arc of constant radius.

[1]
Question 40
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A beam of singly charged positive ions passes through a velocity selector. The uniform electric field has magnitude 1.8×104 V m−11.8\times 10^4\ \text{V m}^{-1} and is directed vertically downward. A uniform magnetic field of magnitude 7.5×10−3 T7.5\times 10^{-3}\ \text{T} is perpendicular to the page. Ions enter the selector horizontally from left to right.

Diagram of a velocity selector with two horizontal plates producing a downward electric field. Positive ions enter from the left with a horizontal velocity arrow. The magnetic field is represented using either dots or crosses throughout the selector, with its direction labelled. The diagram should not show the selected path or deflected paths.
A
I.

Determine the speed of ions that pass through undeflected.

[2]
II.

State the direction of the magnetic field required for the ions in (a)(i) to pass through undeflected.

[1]
B

An ion enters with speed 1.8×106 m s−11.8\times 10^6\ \text{m s}^{-1}. Explain the initial deflection of this ion.

[2]
C

Discuss whether changing the charge of the ions changes the speed selected by this arrangement.

[3]

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Question 41
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

Two long straight parallel wires, AA and BB, are separated by 2.5 cm2.5\ \text{cm}. Wire AA carries a current of 12 A12\ \text{A} and wire BB carries a current of 8.0 A8.0\ \text{A}. The currents are initially in the same direction. A length 0.75 m0.75\ \text{m} of wire BB is in the uniform central region of the apparatus.

End-on or perspective diagram of two long parallel straight wires labelled A and B with equal spacing marked between them. Arrows on both wires show currents in the same direction. No force arrows are shown.
A
I.

State whether the force between the wires is attractive or repulsive.

[1]
II.

Calculate the force per unit length on wire BB.

[2]
B

Determine the total force on the 0.75 m0.75\ \text{m} length of wire BB.

[1]
C

Discuss how a graph could be used to test the dependence of the force on the separation of the wires.

[4]
Question 42
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A beam of ions is accelerated from rest through a potential difference of 1.20 kV1.20\ \text{kV} and then enters a uniform magnetic field of flux density 0.180 T0.180\ \text{T} at right angles to the field. The circular path in the field has radius 6.5 cm6.5\ \text{cm}.

Schematic of ions accelerated through two plates and then entering a region of uniform magnetic field at right angles. The magnetic region shows a curved circular arc of unknown radius with the radius labelled, but the sign of charge is not indicated by the path labels.
A
I.

Show that qm=2VB2r2\dfrac{q}{m}=\dfrac{2V}{B^2r^2} for the ions.

[2]
II.

Determine the specific charge q/mq/m of the ions.

[2]
B

Assuming the ions are singly charged, determine their mass in atomic mass units. Use 1 u=1.66×10−27 kg1\ \text{u}=1.66\times 10^{-27}\ \text{kg}.

[2]
C

Evaluate one reason why measuring a larger radius can improve the reliability of the specific-charge determination.

[2]
Question 43
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

Electrons are accelerated from rest through a potential difference of 2.5 kV2.5\ \text{kV} and then enter a uniform magnetic field of flux density 2.0×10−3 T2.0\times 10^{-3}\ \text{T}. The angle between the electron velocity and the magnetic field is 30∘30^\circ.

Diagram showing electrons accelerated between plates and then entering a long uniform magnetic-field region. The velocity vector is shown at an angle of $30^\circ$ to the magnetic-field direction (the angle label is between the velocity vector and the field lines). The resulting helical path is not shown.
A
I.

Determine the speed of the electrons as they enter the magnetic field.

[2]
II.

Calculate the magnitude of the magnetic force on an electron as it enters the field.

[1]
B

Explain the shape of the path of the electrons in the magnetic field.

[3]
C

Calculate the radius of the helical path. Use your answer to (a)(i),

[2]
Question 44
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A charged particle leaves a visible track in a cloud chamber placed in a uniform magnetic field of flux density 0.45 T0.45\ \text{T} directed into the page. At one point the particle speed is estimated as 4.5×106 m s−14.5\times 10^6\ \text{m s}^{-1} and the radius of curvature of the track is 7.5 cm7.5\ \text{cm}. The initial velocity at this point is to the right and the track curves upward.

Cloud-chamber style diagram showing a curved track segment in a rectangular region of uniform magnetic field into the page. At one point on the track, a tangent velocity arrow points to the right. The local path bends upward from that point. The approximate radius is indicated with a construction arc but no centre-force arrow is shown.
A
I.

Determine whether the charge of the particle is positive or negative.

[1]
II.

Explain your answer to (a)(i).

[2]
B

Determine the magnitude of the charge-to-mass ratio of the particle.

[2]
C

Discuss why the radius of the track may change along the path even though the magnetic field is uniform.

[2]

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Question 45
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

Three long parallel wires AA, CC and BB are perpendicular to the page and lie on a straight horizontal line. Wire CC is between AA and BB, 4.0 cm4.0\ \text{cm} from AA and 8.0 cm8.0\ \text{cm} from BB. Wires AA and BB carry currents out of the page of 9.0 A9.0\ \text{A} and 12 A12\ \text{A} respectively. Wire CC carries a current of 5.0 A5.0\ \text{A} into the page.

End-on diagram of three wire cross-sections arranged horizontally and labelled A, C and B. A and B show dot symbols for current out of the page; C shows a cross symbol for current into the page. The distances from A to C and from C to B are labelled. No force arrows are shown.
A
I.

State the direction of the force on wire CC due to wire AA.

[1]
II.

Calculate the force per unit length on wire CC due to wire AA.

[2]
III.

State the direction of the force on wire CC due to wire BB.

[1]
B

Determine the magnitude and direction of the resultant force per unit length on wire CC.

[2]
C

Evaluate why the forces on wires AA and BB due to wire CC do not violate Newton's third law, even though their magnitudes are different.

[2]
Question 46
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A rectangular coil has 2020 turns. Each vertical side of the coil has length 4.0 cm4.0\ \text{cm} and lies in a uniform magnetic field of flux density 0.60 T0.60\ \text{T}. A current of 1.5 A1.5\ \text{A} flows in the coil. The current in one vertical side is upward and in the other vertical side is downward.

Front-view diagram of a rectangular current-carrying coil between the pole pieces of a magnet. The magnetic field is horizontal across the coil. Current arrows on the two vertical sides are in opposite directions. The lengths of the vertical sides are labelled. No force arrows or rotation direction are shown.
A
I.

Calculate the magnitude of the force on one vertical side of the coil.

[2]
II.

State why the two vertical sides experience forces in opposite directions.

[1]
B

Explain why the coil can rotate even though the net force on it may be zero.

[2]
C

Discuss the effect of reversing the current in the coil.

[2]
Question 47
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A Bainbridge mass spectrometer uses a velocity selector followed by a uniform magnetic-field analyser. In the selector, E=6.0×103 V m−1E=6.0\times 10^3\ \text{V m}^{-1} and B=3.0×10−2 TB=3.0\times 10^{-2}\ \text{T}. Singly charged carbon ions then enter an analyser field of flux density 8.0×10−2 T8.0\times 10^{-2}\ \text{T} at right angles to the field.

Schematic of a mass spectrometer with a velocity selector followed by a separate magnetic analyser region. The selector shows perpendicular electric and magnetic fields and a straight-through slit. The analyser shows the magnetic field out of the page (dots), so the positively charged ions curve downward to two possible positions on a detector, but without labels identifying the isotope.
A
I.

Determine the speed selected by the velocity selector.

[1]
II.

Calculate the radius of the path of a 12C+^{12}\text{C}^+ ion in the analyser. Use m(12C)=1.99×10−26 kgm(^{12}\text{C})=1.99\times 10^{-26}\ \text{kg}.

[2]
B

A 13C+^{13}\text{C}^+ ion enters the analyser with the same selected speed. Compare the paths of the two isotopes in the analyser.

[2]
C

Evaluate two factors that limit the ability of this spectrometer to resolve the two isotope beams.

[3]
Question 48
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

An alpha particle of charge +3.20×10−19 C+3.20\times10^{-19}\ \text{C} and mass 6.64×10−27 kg6.64\times10^{-27}\ \text{kg} enters a region of crossed uniform fields. The electric field has magnitude 4.8×104 V m−14.8\times10^4\ \text{V m}^{-1} and is directed upward. The magnetic field has magnitude 2.0×10−2 T2.0\times10^{-2}\ \text{T} and is directed out of the page. The particle enters horizontally from left to right with speed 1.8×106 m s−11.8\times10^6\ \text{m s}^{-1}. The length of the field region is 12 cm12\ \text{cm}.

Diagram of crossed electric and magnetic fields in a rectangular region. The electric field arrows point upward and the magnetic field is represented by dots out of the page. An alpha particle enters from the left with a horizontal velocity arrow. The field-region length is labelled. No deflected path is drawn.
A
I.

Determine the speed for which an alpha particle would pass undeflected through these fields.

[1]
II.

Calculate the magnitude of the resultant force on the alpha particle as it enters the field region.

[2]
B

Determine the initial direction of deflection of the alpha particle.

[1]
C

Estimate the vertical deflection of the alpha particle while it is within the field region. Assume the horizontal speed remains approximately constant.

[2]
D

Evaluate the approximation that the horizontal speed remains constant in part (c).

[2]

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D.2 Electric and magnetic fields

D.4 Induction