CAIE A-Level Physics A2 20.3 Force on a Moving Charge Questions

Practise analysing magnetic force direction and magnitude, Hall measurements, charged-particle paths and velocity selection in electric and magnetic fields.

Exam points

determine force direction and calculate F=BQv sin theta for moving charges
analyse Hall voltage and Hall-probe measurement
describe charged-particle motion in a uniform magnetic field and apply velocity selection

Covered syllabus points

20.3.1—The direction of the force on a charge moving in a magnetic field 20.3.2—F = BQv sin θ 20.3.3—The origin of the Hall voltage and derive and use the expression V H = BI /20.3.4—The use of a Hall probe to measure magnetic flux density 20.3.5—The motion of a charged particle moving in a uniform magnetic field 20.3.6—How electric and magnetic fields can be used in velocity selection

[Maximum number: 8]

A slice of a conducting material has its face QRLK normal to a uniform magnetic field of flux density B, as illustrated in Fig. 8.1.

Fig. 8.1

Electrons enter the slice travelling perpendicular to face PQKJ.

(a)

For the free electrons moving in the slice:

[ 2 ]

(i)

state the direction of the force on an electron due to movement of the electron in the magnetic field

[ 1 ]

(ii)

identify the faces, using the letters on Fig. 8.1, between which a potential difference is developed.
face and face

[ 1 ]

(b)

Explain why the potential difference in (a)(ii) reaches a maximum value.

[ 2 ]

(c)

The number of free electrons per unit volume in the slice of material is $1.3 \times 10^{29} \mathrm{~m}^{-3}$ . The thickness PQ of the slice is 0.10 mm .
The magnetic flux density B is $4.6 \times 10^{-3} \mathrm{~T}$ .
Calculate the potential difference across the slice for a current of $6.3 \times 10^{-4} \mathrm{~A}$ .
potential difference = V

[ 2 ]

$\begin{aligned} V_{\mathrm{H}} =B I / n t q =\left(4.6 \times 10^{-3} \times 6.3 \times 10^{-4}\right) /\left(1.3 \times 10^{29} \times 0.10 \times 10^{-3} \times 1.60 \times 10^{-19}\right) \end{aligned}$ $=1.4 \times 10^{-12} \mathrm{~V}$

(d)

The slice in (c) is a metal.

By reference to your answer in (c), suggest why Hall probes are usually made using semiconductors rather than metals.

[ 2 ]

semiconductors have a (much) smaller value for n
$V_{\mathrm{H}}$ for semiconductors is (much) larger so more easily measured

[Maximum number: 8]

An electron having charge -q and mass m is accelerated from rest in a vacuum through a potential difference V.
The electron then enters a region of uniform magnetic field of magnetic flux density B, as shown in Fig. 7.1.

Fig. 7.1

The direction of the uniform magnetic field is into the plane of the paper.
The velocity of the electron as it enters the magnetic field is normal to the magnetic field. The radius of the circular path of the electron in the magnetic field is r.

(a)

Explain why the path of the electron in the magnetic field is the arc of a circle.

[ 3 ]

(b)

The potential difference V is 120 V . The radius r of the circular arc is 7.4 cm .

Determine the magnitude B of the magnetic flux density.

[ 3 ]

$\begin{aligned} B q v=m v^{2} / r m v=B q r \text { or } p=B q r \end{aligned}$ $\left(2 \times 9.11 \times 10^{-31} \times 1.60 \times 10^{-19} \times 120\right)^{1 / 2}=B \times 1.60 \times 10^{-19} \times 0.074$ $B=5.0 \times 10^{-4} \mathrm{~T}$

(c)

The potential difference V in (c) is increased. The magnetic flux density B remains unchanged. By reference to the momentum of the electron, explain the effect of this increase on the radius r of the path of the electron in the magnetic field.

[ 2 ]

[Maximum number: 7]

A thin slice of conducting material has its faces PQRS and VWXY normal to a uniform magnetic field of flux density B, as shown in Fig. 9.1.

Fig. 9.1

Electrons enter the slice at right-angles to face SRXY.
A potential difference, the Hall voltage $V_{\mathrm{H}}$ , is developed between two faces of the slice.

(a)

Use letters from Fig. 9.1 to name the two faces between which the Hall voltage is developed. and

[ 1 ]

(b)

State and explain which of the two faces named in (a)(i) is the more positive.

[ 2 ]

(c)

The Hall voltage $V_{\mathrm{H}}$ is given by the expression

V_{\mathrm{H}}=\frac{B I}{n t q} .

[ 4 ]

(i)

Use the letters in Fig. 9.1 to identify the distance t.

[ 1 ]

(ii)

State the meaning of the symbol n.

[ 1 ]

(iii)

State and explain the effect, if any, on the polarity of the Hall voltage when negative charge carriers (electrons) are replaced with positive charge carriers, moving in the same direction towards the slice.

[ 2 ]

[Maximum number: 1]

A slice of a conducting material has its face QRLK normal to a uniform magnetic field of flux density B, as illustrated in Fig. 8.1.

Fig. 8.1

Electrons enter the slice travelling perpendicular to face PQKJ.

For the free electrons moving in the slice:

state the direction of the force on an electron due to movement of the electron in the magnetic field

[Maximum number: 2]

A Hall probe is placed in a magnetic field. The Hall voltage is zero. The Hall probe is rotated to a new position in the magnetic field. The Hall voltage is now maximum.

Explain these observations.

[Maximum number: 2]

An electron is travelling in a vacuum at a speed of $3.4 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$ . The electron enters a region of uniform magnetic field of flux density 3.2 mT , as illustrated in Fig. 8.1.

Fig. 8.1

The initial direction of the electron is at an angle of $30^{\circ}$ to the direction of the magnetic field.

(a)

When the electron enters the magnetic field, the component of its velocity $v_{\mathrm{N}}$ normal to the direction of the magnetic field causes the electron to begin to follow a circular path.

Calculate:

[ 1 ]

(i)

Calculate:
(i) $v_{\mathrm{N}}$

[ 1 ]

$\begin{aligned} v_{\mathrm{N}} =3.4 \times 10^{7} \times \sin 30^{\circ} =1.7 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1} \end{aligned}$

(b)

Use information from (a) and (b) to describe the resultant path of the electron in the magnetic field.

[ 1 ]

[Maximum number: 3]

Explain how a uniform magnetic field and a uniform electric field may be used as a velocity selector for charged particles.

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Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (d)

Question 2

Question (a)

Question (b)

Question (c)

Question 3

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (iii)

Question 4

Question 5

Question 6

Question (a)

Question (i)

Question (b)

Question 7