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D.2 Electric and magnetic fields

Practice exam-style IB Physics questions for Electric and magnetic fields, aligned with the syllabus and grouped by topic.

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

In a Millikan-type experiment, the measured charge on each oil drop must be an integer multiple of the elementary charge ee.

What set of measured charges is consistent with charge quantization?

A.

1.6×10−19 C1.6\times10^{-19}\,\text{C}, 3.2×10−19 C3.2\times10^{-19}\,\text{C}, 4.8×10−19 C4.8\times10^{-19}\,\text{C}

B.

1.6×10−19 C1.6\times10^{-19}\,\text{C}, 2.4×10−19 C2.4\times10^{-19}\,\text{C}, 4.8×10−19 C4.8\times10^{-19}\,\text{C}

C.

0.8×10−19 C0.8\times10^{-19}\,\text{C}, 1.6×10−19 C1.6\times10^{-19}\,\text{C}, 3.2×10−19 C3.2\times10^{-19}\,\text{C}

D.

1.2×10−19 C1.2\times10^{-19}\,\text{C}, 2.4×10−19 C2.4\times10^{-19}\,\text{C}, 3.6×10−19 C3.6\times10^{-19}\,\text{C}

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

Two small charged spheres are separated by a distance rr in air and exert an electrostatic force of magnitude FF on each other. The separation is changed to 2r2r and the spheres are placed in an insulating liquid where the permittivity is three times that of air.

What is the new force magnitude?

A.

F6\dfrac{F}{6}

B.

F12\dfrac{F}{12}

C.

F4\dfrac{F}{4}

D.

3F4\dfrac{3F}{4}

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

A negatively charged plastic rod is brought close to, but does not touch, a neutral metal sphere on an insulating stand. The sphere is then connected briefly to Earth while the rod remains in place. The Earth connection is removed before the rod is taken away.

What is the final charge on the sphere and the charge transfer during earthing?

A.

The sphere is negative; electrons move from Earth to the sphere.

B.

The sphere remains neutral; equal charges move in opposite directions.

C.

The sphere is positive; protons move from Earth to the sphere.

D.

The sphere is positive; electrons move from the sphere to Earth.

Question 4
SL • Paper 1A
Easy
Calculator Permitted
SL • Paper 1A
Easy
Calculator Permitted

A long straight wire is perpendicular to the page and carries conventional current out of the page.

What diagram shows the magnetic field around the wire?

A.
A black-and-white diagram showing a central wire as a circle with a dot symbol indicating current out of the page. Several concentric circular magnetic field lines are centred on the wire. Arrowheads on all circles show an anticlockwise direction. Field-line spacing increases slightly with distance from the wire. Styling is simple and comparable to the other options.
B.
A black-and-white diagram showing a central wire as a circle with a dot symbol indicating current out of the page. Several concentric circular magnetic field lines are centred on the wire. Arrowheads on all circles show a clockwise direction. Field-line spacing increases slightly with distance from the wire. Styling is simple and comparable to the other options.
C.
A black-and-white diagram showing a central wire as a circle with a dot symbol indicating current out of the page. Around it are several straight vertical, parallel magnetic field lines with arrowheads all pointing upward. Styling is simple and comparable to the other options.
D.
A black-and-white diagram showing a central wire as a circle with a dot symbol indicating current out of the page. Straight magnetic field lines radiate outward from the wire in all directions with arrowheads pointing away from the centre. Styling is simple and comparable to the other options.

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Question 5
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
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Two point charges, +3.0 μC+3.0\,\mu\text{C} and −2.0 μC-2.0\,\mu\text{C}, are separated by 0.30 m0.30\,\text{m} in a vacuum.

What is the electric potential energy of the two-charge system?

A.

+0.18 J+0.18\,\text{J}

B.

−0.18 J-0.18\,\text{J}

C.

−0.060 J-0.060\,\text{J}

D.

+0.060 J+0.060\,\text{J}

Question 6
HL • Paper 1A
Easy
Calculator Permitted
HL • Paper 1A
Easy
Calculator Permitted

The diagram shows equipotential lines in a region of an electric field. Adjacent lines differ by the same potential difference.

At which labelled point is the electric field strength greatest?

A two-dimensional equipotential map with several smooth, non-crossing equipotential lines. The lines are closest together near point A, moderately spaced near point B, widely spaced near point C, and evenly but not closely spaced near point D. The points A, B, C and D are marked in clear regions between neighbouring equipotential lines. Adjacent equipotential lines represent equal potential differences. No electric field arrows are drawn.
A.

C

B.

A

C.

B

D.

D

Question 7
SL • Paper 2
Easy
Calculator Permitted
SL • Paper 2
Easy
Calculator Permitted

A negatively charged insulating rod is brought close to a neutral conducting sphere on an insulating stand. The sphere is connected briefly to Earth while the rod remains in position. The Earth connection is then removed before the rod is taken away.

A conducting sphere on an insulating stand is shown near a negatively charged rod without contact. A wire connects the sphere to an Earth symbol. The rod is labelled negative and is positioned to one side of the sphere. No charge distribution is drawn on the sphere.
A

Explain why the sphere is left with a net charge and state the sign of this charge.

[3]
Question 8
SL • Paper 2
Easy
Calculator Permitted
SL • Paper 2
Easy
Calculator Permitted

In a Millikan-type experiment, the measured charges on three oil drops are 3.20×10−19 C3.20\times 10^{-19}\ \text{C}, 4.80×10−19 C4.80\times 10^{-19}\ \text{C} and 6.40×10−19 C6.40\times 10^{-19}\ \text{C}.

A

Deduce the elementary charge from these data and explain how the data support charge quantization.

[2]

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Question 9
SL • Paper 2
Easy
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SL • Paper 2
Easy
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A long straight wire carries a steady conventional current into the plane of the page.

A cross-section diagram of a straight wire represented by a circle with a cross symbol at its centre, indicating conventional current into the page. Several blank circular guide paths may be lightly shown around the wire without arrowheads.
A

State the direction of the magnetic field around the wire and describe how the field strength changes with distance from the wire.

[2]
Question 10
SL • Paper 1A
Medium
Calculator Permitted
SL • Paper 1A
Medium
Calculator Permitted

Two parallel metal plates have a potential difference of 600 V600\,\text{V} and are separated by 3.0 cm3.0\,\text{cm}. A particle of charge +2.0×10−6 C+2.0\times10^{-6}\,\text{C} is between the plates away from edge effects.

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

A.

4.0×10−8 N4.0\times10^{-8}\,\text{N}

B.

3.6×10−5 N3.6\times10^{-5}\,\text{N}

C.

1.2×10−3 N1.2\times10^{-3}\,\text{N}

D.

4.0×10−2 N4.0\times10^{-2}\,\text{N}

Question 11
SL • Paper 1A
Medium
Calculator Permitted
SL • Paper 1A
Medium
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Two equal positive point charges are fixed a small distance apart.

What diagram best represents the electric field lines in the plane containing the charges?

A.
A visually comparable field-line diagram with two identical positive point charges separated horizontally. Field lines are radial around each charge but arrows point inward toward both charges from the surroundings. No field lines connect the charges. The style, line thickness, labels and scale match the other options.
B.
A clean black-and-white field-line diagram with two identical positive point charges separated horizontally. Field lines radiate outward from each charge. Lines between the charges curve away from the midpoint so that no line connects one charge to the other. The pattern is symmetric about the horizontal and vertical midlines, with a small neutral-looking gap at the midpoint. Arrows point away from both charges. Lines never cross.
C.
A visually comparable field-line diagram with two identical positive point charges separated horizontally. Several field lines are drawn directly connecting the two charges across the gap, with arrows from the left charge toward the right charge. Some outer lines radiate outward. The style, line thickness, labels and scale match the other options.
D.
A visually comparable field-line diagram with two identical positive point charges separated horizontally. Lines generally leave the charges, but several lines from the two charges cross each other in the central region between the charges. Arrows point mostly outward. The style, line thickness, labels and scale match the other options.
Question 12
HL • Paper 1A
Medium
Calculator Permitted
HL • Paper 1A
Medium
Calculator Permitted

Four point charges are fixed at the corners of a square. The charges on one diagonal are +Q+Q and +Q+Q. The charges on the other diagonal are −Q-Q and −Q-Q.

What is the electric potential at the centre of the square?

A square with four point charges at its corners. One diagonal pair is labelled $+Q$ and $+Q$; the other diagonal pair is labelled $-Q$ and $-Q$. A point at the centre is labelled $P$. All four corners are the same distance from $P$. No field arrows are shown.
A.

zero

B.

2kQr\dfrac{2kQ}{r}, where rr is the distance from a corner to the centre

C.

4kQr\dfrac{4kQ}{r}, where rr is the distance from a corner to the centre

D.

It cannot be determined without knowing the directions of the electric fields.

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Question 13
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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The electric potential varies along the xx-axis from 12 V12\,\text{V} at x=0.20 mx=0.20\,\text{m} to 4 V4\,\text{V} at x=0.60 mx=0.60\,\text{m}.

What is the average electric field component ExE_x between these points?

A.

−20 V m−1-20\,\text{V m}^{-1}

B.

+40 V m−1+40\,\text{V m}^{-1}

C.

+20 V m−1+20\,\text{V m}^{-1}

D.

−40 V m−1-40\,\text{V m}^{-1}

Question 14
HL • Paper 1A
Medium
Calculator Permitted
HL • Paper 1A
Medium
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An electron is moved from a point at electric potential −3.0 V-3.0\,\text{V} to a point at electric potential +2.0 V+2.0\,\text{V}.

What is the change in electric potential energy of the electron?

A.

−5.0 eV-5.0\,\text{eV}

B.

+5.0 eV+5.0\,\text{eV}

C.

−1.0 eV-1.0\,\text{eV}

D.

+1.0 eV+1.0\,\text{eV}

Question 15
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

Two small charged spheres are fixed in a liquid of relative permittivity 3.03.0. The charges are +4.0 nC+4.0\ \text{nC} and −6.0 nC-6.0\ \text{nC} and their separation is 0.080 m0.080\ \text{m}.

A simple horizontal line diagram showing two small spheres separated by a labelled distance. The left sphere is labelled with a positive charge and the right sphere with a negative charge. The liquid medium is indicated by a lightly shaded rectangular region surrounding both spheres. No force arrows are shown.
A

Calculate the magnitude of the electrostatic force on either sphere and state the direction of the force on the positive sphere.

[2]
Question 16
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

Two large parallel metal plates are separated by 12 mm12\ \text{mm}. The potential difference between the plates is 240 V240\ \text{V}. A small particle with charge +2.0 μC+2.0\ \mu\text{C} is placed midway between the plates, away from the edges.

A side-view diagram of two vertical parallel plates separated by a labelled gap. The left plate is labelled positive and the right plate negative. A small positive charged particle is shown midway between the plates. The potential difference and plate separation are labelled. No field lines or force arrows are shown.
A

Calculate the electric field strength between the plates.

[1]
B

Calculate the force on the particle and state its direction.

[2]

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Question 17
HL • Paper 2
Medium
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HL • Paper 2
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Two point charges are fixed in a vacuum. The charges are +4.0 nC+4.0\ \text{nC} and −2.0 nC-2.0\ \text{nC} and their separation is 0.050 m0.050\ \text{m}.

A horizontal diagram showing two fixed point charges separated by a labelled distance. One charge is positive and the other is negative. No force arrows or energy annotations are shown.
A

Calculate the electric potential energy of the two-charge system and explain the meaning of its sign.

[3]
Question 18
HL • Paper 2
Medium
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HL • Paper 2
Medium
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Point PP is 0.20 m0.20\ \text{m} from a charge of +6.0 nC+6.0\ \text{nC} and 0.10 m0.10\ \text{m} from a charge of −3.0 nC-3.0\ \text{nC}.

A triangular arrangement showing two point charges and point P. Each charge is joined to P by a labelled distance line. The signs of the charges are labelled. No field arrows or equipotential lines are shown.
A

Calculate the electric potential at point PP due to the two charges.

[2]
Question 19
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

Points PP and QQ lie on the same equipotential line in an electric field. A small positive charge is moved slowly from PP to QQ along this line.

A two-dimensional field map showing several smooth equipotential lines. Points P and Q are marked on the same equipotential line. A few electric field lines cross the equipotential lines, but no work or force annotations are included.
A

Explain why no work is done in moving the charge from PP to QQ.

[2]
Question 20
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
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Three identical metal spheres on insulating stands are used in two electrostatics procedures. The charge on each sphere is measured before and after contact or grounding.

An annotated sequence of diagrams. In the first sequence, identical metal spheres A and B are shown before contact, touching, and then separated, with only the initial charge readings displayed; the final charges are left unlabeled. In the second sequence, neutral sphere C is shown near a negatively charged rod, then connected to ground while the rod remains nearby, then disconnected from ground before the rod is removed. Charge meter readings are shown where appropriate, and electron-flow arrows are included only for the grounding stage.
A

Determine the final charge on each of spheres A and B after they touch and are separated.

[1]
B

State the sign of the final charge on sphere C after the induction procedure.

[1]
C

Explain the role of grounding in the induction procedure shown.

[2]

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Question 21
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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A pair of large parallel metal plates is connected to a high-voltage supply. A singly charged positive ion is moved from the positive plate to the negative plate through the central uniform region.

A side-view diagram of two large, oppositely charged parallel plates with a labelled potential difference and plate separation. Straight, equally spaced field lines are drawn in the central region from the positive plate to the negative plate, with slight curvature near the edges. A singly charged positive ion is shown at the positive plate with an arrow indicating motion across the gap.
A

Calculate the electric field strength between the plates in the central region.

[1]
B

Determine the electric force on the ion, including its direction.

[2]
C

Determine the energy transferred to the ion as it moves across the full potential difference. Give your answer in joules and in electronvolts.

[2]
Question 22
HL • Paper 1A
Medium
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HL • Paper 1A
Medium
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A hollow conducting sphere carries a positive charge and contains no charge inside its cavity. The zero of electric potential is at infinity.

What pair of graphs shows the variation with distance rr from the centre of the sphere of the electric field strength EE and the electric potential VeV_e?

A.
Two side-by-side graph panels with a common horizontal axis labelled $r$ and a marked vertical line for the sphere radius. Left panel labelled $E$: the graph lies on the horizontal axis at zero from the centre to the sphere radius, then jumps to a positive surface value and decreases smoothly toward zero with inverse-square-like curvature outside. Right panel labelled $V_e$: the graph is a horizontal positive line from the centre to the sphere radius, then decreases smoothly toward zero with inverse-distance-like curvature outside. Axes and line style match the other options.
B.
Two side-by-side graph panels with horizontal axes labelled $r$ and a marked sphere radius. Left panel labelled $E$: a large positive curve near the centre decreases continuously with inverse-square-like curvature across both inside and outside regions. Right panel labelled $V_e$: a large positive curve near the centre decreases continuously with inverse-distance-like curvature across both inside and outside regions. Axes and line style match the other options.
C.
Two side-by-side graph panels with horizontal axes labelled $r$ and a marked sphere radius. Left panel labelled $E$: the graph starts at zero at the centre and rises linearly up to the sphere radius, then decreases smoothly outside. Right panel labelled $V_e$: the graph decreases slightly inside and then becomes a horizontal positive line outside. Axes and line style match the other options.
D.
Two side-by-side graph panels with horizontal axes labelled $r$ and a marked sphere radius. Left panel labelled $E$: the graph is zero from the centre to the sphere radius, then decreases smoothly outside. Right panel labelled $V_e$: the graph lies on the horizontal axis at zero from the centre to the sphere radius, then rises abruptly at the sphere radius before decreasing smoothly outside. Axes and line style match the other options.
Question 23
SL • Paper 2
Medium
Calculator Permitted
SL • Paper 2
Medium
Calculator Permitted

A hollow conducting sphere has a positive net charge and is in electrostatic equilibrium. The diagram shows a cross-section of the sphere.

A blank cross-section of a hollow conducting sphere, shown as two concentric circles representing the outer and inner surfaces. The conducting material is lightly shaded between the circles. The sphere is labelled positively charged. No field lines or arrows are drawn.
A

Sketch the electric field lines for the sphere, both outside the sphere and inside the hollow region.

[2]
Question 24
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

The graph shows the variation of electric potential VeV_e with position xx between two parallel plates. The potential decreases uniformly from 300 V300\ \text{V} at x=0x=0 to 60 V60\ \text{V} at x=0.080 mx=0.080\ \text{m}.

Electric potential varies linearly with position between parallel plates.
A

Determine the electric field strength between the plates, including its direction along the xx-axis.

[2]

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Question 25
HL • Paper 2
Medium
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HL • Paper 2
Medium
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An electron is moved from a point where the electric potential is +20 V+20\ \text{V} to a point where the electric potential is −30 V-30\ \text{V}.

A

Calculate the change in electric potential energy of the electron in joules and in electronvolts.

[2]
B

State whether the electric potential energy of the electron-field system increases or decreases.

[1]
Question 26
HL • Paper 2
Medium
Calculator Permitted
HL • Paper 2
Medium
Calculator Permitted

A hollow conducting sphere of radius 0.15 m0.15\ \text{m} carries a charge of +5.0 nC+5.0\ \text{nC}. There is no charge inside the hollow region.

A cross-section of a hollow conducting sphere with the radius labelled from the centre to the outer surface. The hollow region is shown clearly. The total positive charge of the sphere is labelled. No electric field lines or equipotential lines are drawn.
A

State the electric field strength inside the hollow region.

[1]
B

Calculate the electric potential at the centre of the hollow region.

[2]
Question 27
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
Calculator Permitted

Two small conducting spheres carry fixed charges and are placed at different separations. The force sensor records the magnitude of the electrostatic force in air and then with the spheres immersed in an insulating oil.

Electrostatic force measured for fixed charges in air and in insulating oil at several values of 1/$\text{r}^{2}$.
A

Describe the relationship between the force in air and the separation of the charged spheres.

[1]
B

Use the air data to determine the magnitude ∣q1q2∣|q_1q_2| of the charges on the spheres.

[2]
C

Explain why the force readings in the insulating oil are smaller than those in air for the same separation.

[2]
Question 28
SL • Paper 1B
Medium
Calculator Permitted
SL • Paper 1B
Medium
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In a Millikan-type experiment, several oil drops are held stationary between horizontal plates by adjusting the potential difference. The charge calculated for each drop is shown.

Oil drop

Charge / C

1

−1.6×10−19-1.6 \times 10^{-19}

2

−3.2×10−19-3.2 \times 10^{-19}

3

−4.8×10−19-4.8 \times 10^{-19}

4

−6.4×10−19-6.4 \times 10^{-19}

5

−8.0×10−19-8.0 \times 10^{-19}

6

−9.6×10−19-9.6 \times 10^{-19}

A

Use the data to estimate the elementary charge.

[1]
B

Determine the number of excess electrons on the drop with charge −6.4×10−19 C-6.4 \times 10^{-19}\ \text{C}.

[1]
C

Explain how these data support the conclusion that charge is quantized.

[2]

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Question 29
SL • Paper 1B
Medium
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SL • Paper 1B
Medium
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A vertical straight wire passes through a horizontal card. Small plotting compasses are placed at different positions around the wire while a steady conventional current flows.

A top-view diagram of a vertical wire through a card with concentric circular guide lines around the wire. Plotting compasses at several positions have their north-seeking ends aligned tangentially to the circular field pattern. A small table beside the diagram shows compass deflection angle at different distances from the wire. A second small inset shows an air-core solenoid with labelled current direction and field lines inside and outside.
A

Determine the direction of the conventional current in the straight wire.

[1]
B

Describe how the magnetic field strength changes with distance from the wire.

[1]
C

Suggest two changes that would increase the magnetic field strength inside the air-core solenoid.

[2]
Question 30
HL • Paper 1B
Medium
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HL • Paper 1B
Medium
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The electric potential is measured at different distances from an isolated point charge. The zero of potential is taken to be at infinity.

Electric potential against distance from a point charge with a tangent line.
A

State the sign of the point charge.

[1]
B

Use the graph to determine the magnitude of the point charge.

[2]
C

Use the tangent to determine the electric field strength at the labelled distance, including direction.

[2]
Question 31
HL • Paper 1B
Medium
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HL • Paper 1B
Medium
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A conducting-paper experiment is used to map electric potentials between two metal electrodes of different shapes. Several equipotential lines are drawn from voltmeter readings.

A conducting-paper map with two labelled electrodes connected to a low-voltage supply. Curved equipotential lines labelled with voltage values span the region between the electrodes. Points P, Q and R are marked; P lies where adjacent equipotentials are close together, Q lies on the same equipotential as R, and arrows for possible field directions are not shown. A scale bar is included.
A

Determine the work done in moving a +3.0 nC+3.0\ \text{nC} test charge from Q to R.

[1]
B

State the direction of the electric field at P relative to the equipotential line through P.

[1]
C

Estimate the magnitude of the electric field strength at P.

[2]
D

Explain why the field is strongest near P.

[1]
Question 32
SL • Paper 1B
Hard
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SL • Paper 1B
Hard
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A charged hollow conducting sphere is isolated from its surroundings. Measurements of electric field strength are made at different distances from the centre of the sphere.

Distance from centre / m

Electric field strength / N C−1^{-1}

0.05

0

0.10

0

0.15

0

0.20

4500

0.30

2000

0.40

1125

A

State the electric field strength inside the hollow region of the sphere.

[1]
B

Use the external field data to determine the magnitude of the charge on the sphere.

[2]
C

Explain why the field is zero inside the hollow conductor but not zero outside it.

[2]

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Question 33
HL • Paper 1B
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HL • Paper 1B
Hard
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Three point charges are fixed at the corners of a triangle. The electric potential energy of the system is found by assembling the charges from infinite separation.

A labelled triangle with point charges at the three vertices. A table beside the diagram gives the charge values at A, B and C and the three side lengths. The charges include both positive and negative values. Units for charge and distance are shown.
A

Calculate the electric potential energy of the pair of charges at A and B.

[1]
B

Determine the total electric potential energy of the three-charge system.

[2]
C

Explain the meaning of the negative value for the total electric potential energy.

[1]
Question 34
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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A charged solid conducting sphere is isolated in air. The electric potential is measured along a radial line from the centre of the sphere.

Electric potential along radial distance from a charged conducting sphere.
A

Use the graph to determine the radius of the conducting sphere.

[1]
B

Determine the charge on the sphere.

[2]
C

Use the graph to compare the electric field strength inside the sphere with that just outside its surface.

[2]
Question 35
HL • Paper 1B
Hard
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HL • Paper 1B
Hard
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The potential between two parallel plates is measured along a line perpendicular to the plates. Measurements are also taken close to one edge of the plates.

Potential along centre and near-edge lines between two plates.
A

Determine the electric field strength in the central region, including its direction.

[2]
B

Calculate the change in electric potential energy of an electron moved from the negative plate to the positive plate.

[2]
C

Evaluate whether the central value of electric field strength is a valid estimate near the edge of the plates.

[1]
Question 36
SL • Paper 2
Hard
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SL • Paper 2
Hard
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Two small insulating spheres carry charges +3.2 μC+3.2\ \mu\text{C} and −1.8 μC-1.8\ \mu\text{C}. The centres of the spheres are separated by 0.24 m0.24\ \text{m} in air. The spheres may be treated as point charges.

A horizontal line diagram showing two small labelled charged spheres separated by a dimension arrow. The left sphere is labelled $+3.2\ \mu\text{C}$, the right sphere is labelled $-1.8\ \mu\text{C}$, and the centre-to-centre separation is labelled $0.24\ \text{m}$. A point midway between the spheres is marked $M$ but no force or field arrows are shown.
A

The electrostatic interaction between the two spheres is considered.

I.

Calculate the magnitude of the force on either sphere.

[2]
II.

Explain the direction of the force on each sphere.

[2]
B

The spheres are immersed in an oil for which the permittivity is 2.52.5 times the permittivity of air. The separation and charges are unchanged. Discuss the effect on the force and on the subsequent motion if the spheres are released from rest.

[3]

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

A negatively charged insulating rod is brought near an isolated neutral metal sphere on an insulating stand. A student then connects the sphere briefly to Earth using a conducting wire, removes the wire, and finally removes the rod.

Three-stage electrostatic induction diagram. Stage 1 shows a negatively charged rod near the left side of a neutral metal sphere on an insulating stand. Stage 2 shows the sphere grounded by a wire while the rod remains nearby. Stage 3 shows the sphere after both wire and rod have been removed. No final charge sign is indicated.
A

The charging process is analysed.

I.

Explain the distribution of charge on the sphere just before it is connected to Earth.

[2]
II.

Explain why the sphere is left with a positive charge at the end of the process.

[2]
B

The student claims that positive charge has been created in the sphere. Evaluate this claim.

[3]
Question 38
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A hollow conducting sphere is mounted on an insulating support. A small positive charge is placed outside the sphere. No charge is placed inside the hollow cavity.

A cross-section of a hollow conducting sphere with a clearly labelled conducting shell and empty cavity. A small positive point charge is shown outside the sphere to one side. Points A inside the cavity, B within the conducting material, and C just outside the outer surface are marked. No field lines are drawn.
A

The electric field in and near the conductor is considered.

I.

State the electric field strength at point B within the conducting material when electrostatic equilibrium has been reached.

[1]
II.

Explain why the electric field at the surface of the conductor is perpendicular to the surface.

[2]
III.

State the electric field strength at point A in the empty cavity.

[1]
B

Discuss how the field-line pattern outside the conducting sphere differs from that around an isolated positive point charge.

[3]
Question 39
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

A long straight wire, a circular coil and an air-core solenoid each carry a steady conventional current. A small plotting compass is used to investigate the magnetic field patterns.

A composite diagram with three separate labelled apparatus sketches: a vertical straight wire passing through a card, a circular current-carrying coil viewed from the front, and a long air-core solenoid viewed from the side. Current directions are indicated on each apparatus. No magnetic field lines are drawn.
A

The magnetic field near the straight wire is considered.

I.

Describe the shape of the magnetic field lines around the straight wire.

[1]
II.

Explain how the direction of the magnetic field is determined from the current direction.

[2]
III.

State how the spacing of field lines changes with distance from the wire.

[1]
B

Compare and contrast the field pattern of the circular coil with that of the air-core solenoid.

[3]
Question 40
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A hollow conducting sphere of radius 0.12 m0.12\ \text{m} carries a total charge of +8.0 nC+8.0\ \text{nC}. There is no charge inside the cavity. The electric potential is defined to be zero at infinity.

A cross-sectional diagram of a charged hollow conducting sphere. The outer radius is labelled $0.12\ \text{m}$ and the sphere is labelled total charge $+8.0\ \text{nC}$. Points A at the centre of the cavity, B on the conducting material, and C outside the sphere are marked. No equipotential lines or field lines are drawn.
A

The potential of the charged conducting sphere is considered.

I.

Calculate the electric potential at the outer surface of the sphere.

[2]
II.

State the electric potential at point A in the cavity.

[1]
III.

Explain why no work is done in moving a small test charge slowly from A to B.

[1]
B

Discuss the shapes of the equipotential surfaces inside and outside the charged hollow conductor.

[3]

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Question 41
HL • Paper 1B
Hard
Calculator Permitted
HL • Paper 1B
Hard
Calculator Permitted

Two fixed point charges produce the equipotential pattern shown. A point P is located between the charges, and several field regions are labelled.

A two-dimensional equipotential map for two point charges of unequal magnitude and opposite sign. The charges are labelled with their charge values. Curved equipotential lines are labelled with potential values and are closer together near the larger-magnitude charge. Point P is marked between the charges with its distances to both charges shown. Regions A, B and C are labelled for comparison of equipotential spacing.
A

Identify the labelled region where the electric field strength is greatest.

[1]
B

Calculate the electric potential at P.

[2]
C

Explain why the electric field at P is not necessarily zero even though the electric potential at P is zero.

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

In a simplified Millikan-type experiment, an oil drop is held stationary between two horizontal parallel plates separated by 6.0 mm6.0\ \text{mm}. The potential difference between the plates is 510 V510\ \text{V}. The effective weight of the drop, including buoyancy correction, is 1.36×10−14 N1.36\times10^{-14}\ \text{N}.

A vertical cross-section of two horizontal parallel plates. The upper plate is labelled positive and the lower plate negative. A small oil drop is shown between the plates. The plate separation is labelled $6.0\ \text{mm}$ and the potential difference is labelled $510\ \text{V}$. No force arrows or charge value are shown.
A

The drop is stationary between the plates.

I.

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

[2]
II.

Calculate the charge on the drop.

[2]
III.

State the sign of the charge on the drop.

[1]
B

Discuss how repeating this experiment for many oil drops provides evidence for quantization of charge.

[3]
Question 43
SL • Paper 2
Hard
Calculator Permitted
SL • Paper 2
Hard
Calculator Permitted

Two large horizontal parallel plates are separated by 12 mm12\ \text{mm} and connected to a 1.8 kV1.8\ \text{kV} supply. A small bead of mass 2.4×10−6 kg2.4\times10^{-6}\ \text{kg} carries a charge of −3.0 nC-3.0\ \text{nC}. The bead is released from rest close to the negative plate.

A side-view diagram of two large horizontal parallel plates. The upper plate is labelled positive and the lower plate negative. The separation is labelled $12\ \text{mm}$ and the potential difference is labelled $1.8\ \text{kV}$. A small negatively charged bead is shown near the lower negative plate. Edge effects are not shown in the central region.
A

Ignore gravitational effects and edge effects.

I.

Calculate the electric field strength between the plates.

[2]
II.

Determine the acceleration of the bead immediately after release.

[2]
III.

State the direction of the electric field between the plates.

[1]
B

Evaluate the statement: “The bead gains 1.8 keV1.8\ \text{keV} of kinetic energy in crossing the plates.”

[3]
Question 44
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

Three point charges are fixed at the vertices of a right-angled triangle. Charge AA is +4.0 μC+4.0\ \mu\text{C}, charge BB is +2.0 μC+2.0\ \mu\text{C} and charge CC is −3.0 μC-3.0\ \mu\text{C}. The distances are AB=0.30 mAB=0.30\ \text{m}, AC=0.40 mAC=0.40\ \text{m} and BC=0.50 mBC=0.50\ \text{m}.

A right-angled triangle diagram. Vertex A is labelled $+4.0\ \mu\text{C}$, vertex B is labelled $+2.0\ \mu\text{C}$ and vertex C is labelled $-3.0\ \mu\text{C}$. The side lengths $AB=0.30\ \text{m}$, $AC=0.40\ \text{m}$ and $BC=0.50\ \text{m}$ are shown. No force arrows or energy values are shown.
A

The electric potential energy of the system is to be determined.

I.

State why electric potential energies of the three pairs can be added algebraically.

[1]
II.

Calculate the total electric potential energy of the three-charge system.

[3]
III.

Interpret the sign of your answer to (a)(ii).

[1]
B

Discuss why using electric potential energy can be more convenient than using forces for this three-charge system.

[3]

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

Two fixed point charges lie on a straight line. Charge Q1=+6.0 μCQ_1=+6.0\ \mu\text{C} is at x=0x=0 and charge Q2=−2.0 μCQ_2=-2.0\ \mu\text{C} is at x=0.40 mx=0.40\ \text{m}. Point PP lies on the line between the two charges.

A horizontal x-axis line with $Q_1=+6.0\ \mu\text{C}$ at the left labelled $x=0$, $Q_2=-2.0\ \mu\text{C}$ to the right labelled $x=0.40\ \text{m}$, and a movable point P between them. No field or potential arrows are drawn.
A

Electric potential along the line is considered.

I.

State why electric potential at a point due to the two charges is found by algebraic addition.

[1]
II.

Determine the position between the charges where the electric potential is zero.

[3]
B

Evaluate the claim: “At the point where the electric potential is zero, the electric field strength must also be zero.”

[3]
Question 46
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

The graph shows the variation of electric potential VeV_e with position xx along a line between two large parallel plates. Edge effects are negligible.

Electric potential varies linearly with position between parallel plates.
A

Information is obtained from the potential-position graph.

I.

Explain why the electric field between the plates is uniform.

[2]
II.

Determine the magnitude and direction of the electric field if the potential decreases by 120 V120\ \text{V} over 4.0 cm4.0\ \text{cm}.

[3]
B

An electron is released from rest near the lower-potential plate. Discuss the changes to the electron's electric potential energy and kinetic energy as it moves.

[3]
Question 47
HL • Paper 2
Hard
Calculator Permitted
HL • Paper 2
Hard
Calculator Permitted

A conducting-paper experiment is used to map the equipotentials between two long, oppositely charged parallel electrodes. The electrodes are separated by 5.0 cm5.0\ \text{cm} and connected to a 10.0 V10.0\ \text{V} supply.

A top-view diagram of conducting paper with two long parallel straight electrodes separated by a labelled distance of $5.0\ \text{cm}$. The left electrode is labelled $+10.0\ \text{V}$ and the right electrode is labelled $0\ \text{V}$. Several blank points are available between the electrodes for plotting equipotentials, but no equipotential or field lines are drawn.
A

The central region between the electrodes is assumed to be uniform.

I.

Determine the electric field strength in the central region.

[2]
II.

On the diagram, draw the 6.0 V6.0\ \text{V} equipotential line in the central region.

[2]
III.

State the angle between electric field lines and equipotential lines.

[1]
B

Evaluate why the measured equipotentials near the ends of the electrodes may not be equally spaced straight lines.

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

Four identical point charges are fixed at the corners of a square of side 0.20 m0.20\ \text{m}. The two charges on the left are +Q+Q and the two charges on the right are −Q-Q, where Q=2.0 μCQ=2.0\ \mu\text{C}. Point O is at the centre of the square.

A square with side length labelled $0.20\ \text{m}$. The two left-hand corners are labelled $+Q$ and the two right-hand corners are labelled $-Q$. The centre of the square is marked O. A vertical line through O and a horizontal line through O are lightly shown as symmetry axes. No field arrows or equipotentials are drawn.
A

The potential and field at O are considered.

I.

Deduce the electric potential at O.

[2]
II.

Discuss whether the electric field strength at O is zero.

[3]
B

A student sketches equipotential lines for the arrangement and draws one equipotential line crossing another. Evaluate the student's sketch.

[3]

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D.1 Gravitational fields

D.3 Motion in electromagnetic fields