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.
Question 1
A proton is released from rest between two large parallel plates. The uniform electric field is directed vertically upwards. What is the initial motion of the proton?
A.
It accelerates upwards with constant acceleration.
B.
It remains at rest because the field is uniform.
C.
It moves upwards with constant speed.
D.
It accelerates downwards with constant acceleration.
Question 2
A charged particle of speed v enters a magnetic field B at an angle θ to the field. What is the magnitude of the magnetic force on the particle?
A.
qvB cos θ
B.
qv/B sin θ
C.
qvB sin θ
D.
qB/v sin θ
Question 3
A straight wire carries current I in a uniform magnetic field. The angle between the wire and the magnetic field is 30°. What expression gives the magnitude of the force on length L of the wire?
A.
BIL sin 30°
B.
BI/L sin 30°
C.
BIL
D.
BIL cos 30°
Question 4
A charged particle moves in a circle in a uniform magnetic field.
State the direction of the magnetic force relative to the particle's velocity.
[1]
Explain why the speed of the particle remains constant.
[1]
Question 5
A long straight vertical wire carries a steady current upwards.
Describe the shape of the magnetic field lines around the wire.
[1]
State the rule used to determine their direction.
[1]
Question 6
An electron enters a uniform magnetic field at right angles to the field. The field is into the page and the electron initially moves to the right. What happens to the kinetic energy of the electron while it remains in the field?
A.
It decreases because the magnetic force is centripetal.
B.
It increases because the magnetic force accelerates the electron.
C.
It remains constant because the magnetic force is perpendicular to the velocity.
D.
It oscillates because the force reverses every half turn.
Question 7
In a velocity selector the electric field strength is 4.0 × 10³ V m⁻¹ and the magnetic flux density is 2.0 × 10⁻² T. What speed passes through undeflected?
A.
5.0 × 10⁻⁶ m s⁻¹
B.
8.0 × 10⁵ m s⁻¹
C.
2.0 × 10⁵ m s⁻¹
D.
8.0 × 10¹ m s⁻¹
Question 8
Two long parallel wires carry currents in opposite directions. What is the magnetic force between the wires?
A.
Repulsive, with equal magnitude forces on the two wires.
B.
Repulsive, with the larger force on the wire carrying the larger current.
C.
Attractive, with equal magnitude forces on the two wires.
D.
Zero, because the magnetic fields cancel between the wires.
Question 9
An electron enters a uniform electric field with its velocity initially perpendicular to the field. Air resistance is negligible. What is the shape of its path while it is between the plates?
A.
Helical
B.
Parabolic
C.
Circular
D.
Straight
Question 10
A charged particle enters a uniform magnetic field with a velocity that has both parallel and perpendicular components to the field. What is the resulting path?
A.
A helix with constant pitch
B.
A circle in a plane perpendicular to the field
C.
A straight line parallel to the magnetic field
D.
A parabola in a plane containing the field
Question 11
What is the direction of the magnetic field at a point due east of a long vertical wire carrying conventional current upwards?
A.
Upwards
B.
North
C.
South
D.
Downwards
Question 12
A current-carrying wire is parallel to a uniform magnetic field. What is the magnetic force on the wire?
A.
BIL/2
B.
BIL
C.
Zero
D.
It depends on the sign of the charge carriers only.
Question 13
An electron enters a region between parallel plates with horizontal speed 2.0 × 10⁷ m s⁻¹. The uniform electric field between the plates is 3.5 × 10⁴ N C⁻¹ vertically downwards. The length of the plates is 4.0 cm.
Calculate the time for the electron to pass through the plates.
[1]
Calculate the magnitude of the electron's acceleration due to the electric field.
[1]
State the direction of the electron's deflection.
[1]
Question 14
A velocity selector has perpendicular uniform electric and magnetic fields. The electric field strength is 6.0 × 10⁴ V m⁻¹ and the magnetic flux density is 0.15 T.
State the condition for a charged particle to pass undeflected.
[1]
Calculate the selected speed.
[1]
Question 15
A straight wire of length 5.0 cm is placed at right angles to a uniform magnetic field of flux density 0.80 T. The current in the wire is 3.0 A.
Calculate the force on the wire.
[1]
State one change that would reverse the direction of the force.
[1]
State the effect on the force magnitude of rotating the wire until it is parallel to the field.
[1]
Question 16
A beam of electrons and a beam of positrons enter the same uniform magnetic field with the same velocity perpendicular to the field.
Compare the magnitudes of the magnetic forces on the particles.
[1]
Compare the directions of curvature of the paths.
[1]
Question 17
A student investigates the deflection of electrons between parallel plates. The electrons enter horizontally with the same speed each time. The plate length X is varied while the electric field is kept constant.
Using the graph, describe the relationship between vertical deflection s and plate length X.
[1]
Explain why the horizontal component of velocity is unchanged between the plates.
[1]
The student plots s against X². State the feature of this plot that would support the model of constant vertical acceleration.
[1]
Suggest one reason why the data may not follow the model for the largest plate lengths.
[1]
Question 18
A wire placed at right angles to a uniform magnetic field is connected to a variable power supply. A balance is used to measure the magnetic force for different currents.
State the relationship between force and current shown by the graph.
[1]
Use the gradient of a force-current graph to state how the magnetic flux density B could be found.
[1]
Suggest why measurements for positive and negative current are useful.
[1]
Identify one controlled variable required for this investigation.
[1]
Question 19
Tracks of charged particles are photographed in a uniform magnetic field directed out of the page. The particles enter with the same speed perpendicular to the field.
State which track corresponds to the particle with the greatest momentum per unit charge.
[1]
Explain your answer to (a).
[1]
State what can be inferred from the opposite curvature of two tracks.
[1]
Question 20
A singly charged ion of mass m and speed v moves at right angles to a uniform magnetic field B in a circle of radius r. If the speed is doubled and B is unchanged, what is the new radius?
A.
r/2
B.
4r
C.
2r
D.
r
Question 21
Electrons are accelerated from rest through a potential difference V and then enter a uniform magnetic field B at right angles. What is proportional to the radius of their circular path?
A.
√V / B
B.
V
C.
V / B²
D.
B / √V
Question 22
The separation of two long parallel wires carrying unchanged currents is doubled. What happens to the force per unit length between the wires?
A.
It remains unchanged.
B.
It becomes one quarter of its original value.
C.
It becomes one half of its original value.
D.
It doubles.
Question 23
A positive ion moves north in a horizontal magnetic field directed east. What is the direction of the magnetic force on the ion?
A.
South
B.
Downwards
C.
Upwards
D.
West
Question 24
Singly charged ions pass undeflected through a velocity selector and then enter a magnetic field-only region. Ions of greater mass but the same charge will strike a detector at a position corresponding to
A.
no circular path because magnetic fields only act on electrons.
B.
a larger radius because r = mv/qB.
C.
the same radius because the velocity selector removes mass dependence.
D.
a smaller radius because their selected speed is smaller.
Question 25
A charged particle is accelerated from rest through a potential difference V. If the potential difference is increased to 4V, what happens to the final speed of the particle?
A.
It is unchanged because charge is quantized.
B.
It becomes 4 times larger.
C.
It becomes 2 times larger.
D.
It becomes 8 times larger.
Question 26
A proton of speed 3.0 × 10⁶ m s⁻¹ enters a uniform magnetic field of flux density 0.20 T at right angles.
Calculate the magnetic force on the proton.
[1]
Calculate the radius of its circular path.
[1]
Question 27
Two long parallel wires separated by 4.0 cm carry currents of 6.0 A and 8.0 A in the same direction.
State whether the force between the wires is attractive or repulsive.
[1]
Calculate the force per unit length on either wire.
[1]
Question 28
A beam of alpha particles is directed horizontally between two horizontal parallel plates. The upper plate is positive and the lower plate is negative.
State the direction of the electric field between the plates.
[1]
State the direction of the force on an alpha particle.
[1]
Explain why the path is curved but not circular.
[1]
Question 29
A positive ion enters a uniform magnetic field with velocity at 40° to the field direction.
State which component of the ion's velocity is unchanged by the magnetic field.
[1]
Explain the resulting motion of the ion.
[1]
Question 30
A proton and an electron are separately released from rest in the same uniform electric field.
Compare the directions of their accelerations.
[1]
Compare the magnitudes of the electric forces on them.
[1]
Compare the magnitudes of their accelerations.
[1]
Question 31
A horizontal wire of length 0.12 m carries a current of 4.0 A towards the east. It is in a uniform magnetic field of flux density 0.50 T directed north.
Calculate the magnitude of the force on the wire.
[1]
Determine the direction of the force.
[1]
State the direction of the force if the current is reversed.
[1]
Question 32
Two long parallel wires carry equal currents in the same direction. The force per unit length is measured for different separations.
Describe how the force per unit length changes as separation increases.
[1]
State the transformation of the separation data that should give a straight-line graph.
[1]
Explain why the force on the two wires has the same magnitude.
[1]
Use the relationship for parallel wires to explain how doubling both currents would affect the force per unit length at the same separation.
[1]
Question 33
A beam of positive ions enters crossed electric and magnetic fields. The magnetic field is kept constant while the electric field is varied. A detector records the beam position after the field region.
Identify from the graph the condition corresponding to zero deflection.
[1]
Explain why only one ion speed is undeflected for a given pair of field strengths.
[1]
State how the selected speed changes if the electric field strength is increased while B is constant.
[1]
Question 34
A sensor measures the magnetic force on identical positive ions moving at the same speed through a uniform magnetic field. The angle θ between the velocity and the magnetic field is varied.
State the angle at which the measured force is maximum.
[1]
State the angle at which the measured force is zero.
[1]
Explain how the graph supports the relationship F = qvB sin θ.
[1]
Suggest why measurements near θ = 0° have a large percentage uncertainty.
[1]
Question 35
Electrons are accelerated from rest through a potential difference of 250 V and then enter a uniform magnetic field of flux density 1.8 × 10⁻³ T at right angles.
Calculate the speed of the electrons after acceleration.
[1]
Calculate the radius of the path in the magnetic field.
[1]
Question 36
A singly charged positive ion passes undeflected through crossed electric and magnetic fields. The electric field is 2.4 × 10⁴ V m⁻¹ and the magnetic field is 0.080 T. The ion then enters a magnetic field of 0.120 T and follows a circular path of radius 0.18 m.
Determine the speed selected by the crossed fields.
[1]
Determine the mass of the ion.
[1]
Question 37
A long straight wire carries a current of 12 A.
Calculate the magnetic flux density at a distance of 3.0 cm from the wire.
[1]
second parallel wire carrying 5.0 A is placed at this distance. Calculate the force per unit length on the second wire.
[1]
Question 38
In an experiment to test the force between two parallel current-carrying wires, the currents are kept constant while the separation is varied.
State the graph that should be plotted to test the predicted dependence on separation.
[1]
State the expected shape of this graph.
[1]
Suggest one experimental reason why the graph may deviate from the expected shape at large separations.
[1]
Question 39
In a fine-beam tube experiment, electrons are accelerated from rest through different potential differences V and then enter the same uniform magnetic field B at right angles. The radius r of the circular path is measured.
State why a graph of V against r² should be linear.
[1]
Use the gradient G of the graph of V against r² to write an expression for e/m in terms of B and G.
[1]
Suggest one reason why the measured radius may be systematically too large.
[1]
State the effect of a systematically too large radius on the calculated value of e/m.
[1]
Question 40
A mass spectrometer uses a velocity selector followed by a uniform magnetic field region. The detector position is recorded for singly charged ions from a sample containing two isotopes.
State what the two detector peaks indicate about the sample.
[1]
Explain why the ions have the same speed after the velocity selector.
[1]
Determine which peak corresponds to the heavier isotope.
[1]
Suggest two changes that would increase the separation of the two peaks at the detector.
[1]
Question 41
A probe measures the magnetic flux density B at different distances r from a long straight wire carrying a steady current.
Describe the trend shown by the B against r graph.
[1]
State a graph that would test whether B is proportional to 1/r.
[1]
Explain how the current in the wire could be determined from the gradient of a suitable graph.
[1]
Suggest why the model may fail close to the wire.
[1]
Question 42
A beam of positive ions enters a region where a uniform electric field and a uniform magnetic field are perpendicular to each other and to the initial velocity of the ions.
Derive the condition for an ion to pass through the crossed fields without deflection.
[1]
Explain how this arrangement can be used as a velocity selector and discuss what happens to ions with speeds greater than and less than the selected speed.
[1]
Question 43
A charged particle may enter either a uniform electric field or a uniform magnetic field with its initial velocity perpendicular to the field.
Describe the motion in the uniform electric field.
[1]
Compare and contrast this with the motion in the uniform magnetic field.
[1]
Question 44
A laboratory balance is used to measure the force on a straight current-carrying conductor placed in a uniform magnetic field.
State the relationship between force and the variables for the conductor in the magnetic field.
[1]
Discuss how the experiment could be designed to determine the magnetic flux density and improve the reliability of the result.
[1]
Question 45
A simulation compares the magnitudes of electric and gravitational forces on small particles between parallel plates. The particles have different charge-to-mass ratios q/m in the same uniform electric field.
| Particle | \ | q\ | /m / C kg^-1 | Electric accel. / m s^-2 | g / m s^-2 |
|---|---|---|---|---|---|
| Electron | 1.76×10^11 | 1.76×10^14 | 9.81 | ||
| Proton | 9.58×10^7 | 9.58×10^10 | 9.81 | ||
| Na+ ion | 4.19×10^6 | 4.19×10^9 | 9.81 | ||
| Charged dust grain | 1.5×10^-3 | 1.5 | 9.81 | ||
| Oil droplet | 2.0×10^-5 | 2.0×10^-2 | 9.81 |
State how the acceleration due to the electric field depends on q/m.
[1]
Using the table, identify the particle for which gravitational effects are most significant relative to electric effects.
[1]
Explain why gravity is often neglected for electrons moving in laboratory electric fields.
[1]
Suggest one situation in which neglecting gravity for charged particles might not be justified.
[1]
Question 46
Two long, straight, parallel wires carry steady currents.
Outline how the magnetic field produced by one wire is represented and how its direction is found.
[1]
Explain the origin, direction and magnitude dependence of the force between the two wires.
[1]
Question 47
In a fine-beam tube, electrons are accelerated from rest through a potential difference and then move in a circular path in a uniform magnetic field.
Derive an expression for the specific charge e/m of the electron in terms of accelerating potential difference V, magnetic flux density B and path radius r.
[1]
Evaluate the main assumptions and sources of uncertainty in using this method to determine e/m.
[1]
Question 48
A Bainbridge-type mass spectrometer uses a velocity selector followed by a magnetic analysing region.
Explain the role of the velocity selector.
[1]
Explain how the instrument separates isotopes and how the mass-to-charge ratio can be determined.
[1]
Question 49
Curved tracks of charged particles are observed in a detector placed in a uniform magnetic field.
Explain what can be inferred from the direction and radius of curvature of a track.
[1]
Discuss the limitations of using only a magnetic-field track to identify a particle.
[1]
Question 50
A proposed method to estimate the closest approach of an alpha particle to a positively charged nucleus treats the alpha particle as moving head-on in an electric field and neglects other interactions until the turning point.
Outline the energy principle used to find the closest approach.
[1]
Evaluate the assumptions and significance of this method for probing nuclear size.
[1]
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