IB Physics HL D 2 Electric and Magnetic Fields Questions

Practise IB Physics HL D.2 by analysing charge interactions, electric and magnetic fields, potential energy and electric potential, work, and equipotential patterns.

Exam points

Determine attraction or repulsion and calculate point-charge forces with Coulomb’s law, including superposed forces.
Apply conservation of charge to particle reactions and charge redistribution between objects.
Interpret Millikan’s oil-drop experiment as evidence that electric charge is quantized.
Trace electron transfer to explain charging by contact or friction and the resulting sign of charge.
Calculate electric field strength from force per unit charge and combine field vectors from several sources.
Draw or interpret electric field-line direction and use line density to compare field strength.
Calculate the uniform field between parallel plates from potential difference and separation, then relate it to charge force.
Draw or interpret magnetic-field patterns and directions around magnets and current-carrying wires.
Relate electric potential energy to the work required to assemble a system of charges from infinite separation.
Calculate two-point-charge potential energy with its sign and distinguish it from electric potential.
Treat electric potential as a scalar, combine contributions from charges, and apply the zero-at-infinity reference.
Calculate electric potential around a point charge and use its spatial gradient to determine field strength and direction.
Use work qΔV and equipotential diagrams to analyse energy changes, zero work along an equipotential, and the perpendicular field direction.

Covered syllabus points

D.2.1—Electric charge forces D.2.2—Coulomb’s law D.2.3—Charge conservation D.2.4—Millikan experiment D.2.5—Charge transfer D.2.6—Electric field strength D.2.7—Electric field lines D.2.8—Field-line density D.2.9—Parallel-plate field D.2.10—Magnetic field lines D.2.11 (HL)—Electric potential energy D.2.12 (HL)—Two-charge potential energy D.2.13 (HL)—Electric potential as scalar D.2.14 (HL)—Electric potential D.2.15 (HL)—Electric potential gradient D.2.16 (HL)—Work in electric fields D.2.17 (HL)—Electric equipotentials D.2.18 (HL)—Equipotentials and electric fields

[Maximum number: 2]

Ion-thrust engines can power spacecraft. In this type of engine, ions are created in a chamber and expelled from the spacecraft. The spacecraft is in outer space when the propulsion system is turned on. The spacecraft starts from rest.

The mass of ions ejected each second is $6.6 \times 10^{-6} \mathrm{~kg}$ and the speed of each ion is $5.2 \times 10^{4} \mathrm{~m} \mathrm{~s}^{-1}$ . The initial total mass of the spacecraft and its fuel is 740 kg . Assume that the ions travel away from the spacecraft parallel to its direction of motion.

In practice, the ions leave the spacecraft at a range of angles as shown.

Outline why the ions are likely to spread out.

[Maximum number: 10]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

(a)

Define electric field strength.

[ 2 ]

(b)

(b) The diagram shows a pair of horizontal metal plates. Electrons can be deflected vertically using an electric field between the plates.

[ 4 ]

(i)

Draw the shape and direction of the electric field between the plates on the diagram.

[ 2 ]

(ii)

Calculate the force on an electron between the plates when the electric field strength has a value of $2.5 \times 10^{3} \mathrm{NC}^{-1}$ .

[ 2 ]

$F=2.5 \times 10^{3} \times 1.6 \times 10^{-19}$ ;
$4.0 \times 10^{-16} \mathrm{~N}$ ;

Marking guidance:

Award [2] for a bald correct answer.

(c)

The diagram shows two isolated electrons, X and Y , initially at rest in a vacuum. The initial separation of the electrons is 5.0 mm . The electrons subsequently move apart in the directions shown.

[ 4 ]

(i)

Show that the initial electric force acting on each electron due to the other electron is approximately $9 \times 10^{-24} \mathrm{~N}$ .

[ 2 ]

(c) (i) use of $F=\frac{\left(1.60 \times 10^{-19}\right)^{2}}{4 \pi \varepsilon_{0}\left(5.0 \times 10^{-3}\right)^{2}}$ or $F=\frac{\left(1.60 \times 10^{-19}\right)^{2}}{\left(5.0 \times 10^{-3}\right)^{2}} \times 8.99 \times 10^{9}$ ;
$9.2 \times 10^{-24} \mathrm{~N} ;$

(ii)

The diagram shows Y as seen from X , at one instant. Y is moving into the plane of the paper. For this instant, draw on the diagram the shape and direction of the magnetic field produced by Y .

[ 2 ]

[Maximum number: 1]

Deuterium, ${ }_{1}^{2} \mathrm{H}$ , undergoes fusion according to the following reaction.

{ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \rightarrow{ }_{1}^{3} \mathrm{H}+\mathrm{X}

Particle Y is produced in the collision of a proton with a $\mathrm{K}^{-}$ in the following reaction.

\mathrm{K}^{-}+\mathrm{p}^{+} \rightarrow \mathrm{K}^{0}+\mathrm{K}^{+}+\mathrm{Y}

The quark content of some of the particles involved are

\mathrm{K}^{-}=\overline{\mathrm{u}} \mathrm{~s} \quad \mathrm{~K}^{0}=\mathrm{d} \overline{\mathrm{~s}}

Identify, for particle Y , the

charge.

[Maximum number: 2]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

The diagram shows two isolated electrons, X and Y , initially at rest in a vacuum. The initial separation of the electrons is 5.0 mm . The electrons subsequently move apart in the directions shown.

Show that the initial electric force acting on each electron due to the other electron is approximately $9 \times 10^{-24} \mathrm{~N}$ .

[Maximum number: 1]

Who was the first scientist to show that electric charge is quantized?

Coulomb

Millikan

Planck

Rutherford

[Maximum number: 1]

A conducting sphere has radius 48 cm . The electric potential on the surface of the sphere is $3.4 \times 10^{5} \mathrm{~V}$ .

The sphere is connected by a long conducting wire to a second conducting sphere of radius 24 cm . The second sphere is initially uncharged.

Describe, in terms of electron flow, how the smaller sphere becomes charged.

[Maximum number: 2]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

(b) The diagram shows a pair of horizontal metal plates. Electrons can be deflected vertically using an electric field between the plates.

Draw the shape and direction of the electric field between the plates on the diagram.

[Maximum number: 1]

Electric field lines

can cross each other.

are parallel to equipotential surfaces.

are directed from negative to positive charges.

show field strength by their density.

[Maximum number: 1]

Two oppositely charged parallel plates are a distance 8.0 cm apart. The potential difference between the plates is 120 V . An alpha particle is placed on the positively charged plate and released from rest. Gravity is ignored.

Calculate the electric field between the plates.

$E=<\frac{120}{8.0 \times 10^{-2}}=>1.5 \times 10^{3} N C^{-1} \boldsymbol{O} \boldsymbol{R} \mathrm{Vm}^{-1}$

[Maximum number: 2]

This question is in two parts. Part 1 is about photoelectricity. Part 2 is about electrical and magnetic force fields.
Part 1 Photoelectricity

The diagram shows two isolated electrons, X and Y , initially at rest in a vacuum. The initial separation of the electrons is 5.0 mm . The electrons subsequently move apart in the directions shown.

The diagram shows Y as seen from X , at one instant. Y is moving into the plane of the paper. For this instant, draw on the diagram the shape and direction of the magnetic field produced by Y .

[Maximum number: 1]

An electron is fixed in position in a uniform electric field. What is the position for which the electrical potential energy of the electron is greatest?

[Maximum number: 4]

(a)

In a classical model of the singly-ionized helium atom, a single electron orbits the nucleus in a circular orbit of radius r.

[ 4 ]

(i)

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k e^{2}}{r}$ .

[ 2 ]

uses (a)(i) to state $E_{\mathrm{k}}=\frac{k e^{2}}{r} \mathcal{OR}$ states $E_{\mathrm{p}}=-\frac{2 k e^{2}}{r}$ adds $« E_{\mathrm{TOT}}=E_{\mathrm{k}}+E_{\mathrm{p}}=\frac{k e^{2}}{r}-\frac{2 k e^{2}}{r}$ » to get the result

(ii)

In this model the electron loses energy by emitting electromagnetic waves.

Describe the predicted effect of this emission on the orbital radius of the electron.

[ 2 ]

the total energy decreases OR by reference to $E_{\text {TOT }}=-\frac{k e^{2}}{r}$ the radius must also decrease

Award [0] for an answer concluding that radius increases

[Maximum number: 2]

A vertical wall carries a uniform positive charge on its surface. This produces a uniform horizontal electric field perpendicular to the wall. A small, positively-charged ball is suspended in equilibrium from the vertical wall by a thread of negligible mass.

The centre of the ball, still carrying a charge of $1.2 \times 10^{-6} \mathrm{C}$ , is now placed 0.40 m from a point charge Q . The charge on the ball acts as a point charge at the centre of the ball.
P is the point on the line joining the charges where the electric field strength is zero. The distance PQ is 0.22 m .

Outline, without calculation, whether or not the electric potential at P is zero.

[Maximum number: 2]

A metal sphere is charged positively and placed far away from other charged objects. The electric potential at a point on the surface of the sphere is 53.9 kV .

The electric potential at a point a distance 2.8 m from the centre of the sphere is 7.71 kV . Determine the radius of the sphere.

use of V r= constant $0.40 \mathrm{~m}$

Marking guidance:

Allow [1] max if r+2.8 used to get 0.47 m .

Allow [2] marks if they calculate Q at one potential and use it to get the distance at the other potential.

[Maximum number: 1]

This question is about electric potential and electric field.

A metal sphere of radius 0.080 m is charged to a potential of 300 V .

State the value of the magnitude of the gradient of electric potential at a distance of 0.16 m from the centre of the sphere.

A6. This question is about the motion of a copper rod in a magnetic field.

A copper rod XY is able to move freely along two horizontal, parallel conducting rails A and B . The conducting rails are in a region of uniform magnetic field that is in a direction perpendicular to the plane of the rails. The rails are connected together at one end by a conducting wire.

In the situation shown, the rod is moved along the rails at a constant speed v by a constant horizontal force of magnitude F.

$950 \mathrm{~V} \mathrm{~m}^{-1}$ ;

Marking guidance:

Allow ECF from (b)(ii).

[Maximum number: 2]

This question is in two parts

Ionized hydrogen atoms are accelerated from rest in the vacuum between two vertical parallel conducting plates. The potential difference between the plates is V. As a result of the acceleration each ion gains an energy of $1.9 \times 10^{-18} \mathrm{~J}$ .

Calculate the value of V.

$\quad V=\frac{1.9 \times 10^{-18}}{1.6 \times 10^{-19}}$ ;
$=12 \mathrm{~V}$ ;

[Maximum number: 2]

Hydrogen atoms in an ultraviolet (UV) lamp make transitions from the first excited state to the ground state. Photons are emitted and are incident on a photoelectric surface as shown.

The electric potential of the photoelectric surface is 0 V . The variable voltage is adjusted so that the collecting plate is at -1.2 V .

photoelectric surface

On the diagram, draw and label the equipotential lines at -0.4 V and -0.8 V .

[Maximum number: 1]

A metal sphere is charged positively and placed far away from other charged objects. The electric potential at a point on the surface of the sphere is 53.9 kV .

A small positively charged object moves towards the centre of the metal sphere. When the object is 2.8 m from the centre of the sphere, its speed is $3.1 \mathrm{~ms}^{-1}$ . The mass of the object is 0.14 g and its charge is $2.4 \times 10^{-8} \mathrm{C}$ .

Comment on the angle at which the object meets equipotential surfaces around the sphere.

$90^{\circ}$ / perpendicular

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Covered syllabus points

Question 1

Question 2

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Question (b)

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Question (c)

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Question (ii)

Question 3

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Question 12

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Question 13

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Question 18