Motion of charged particles in B
*Code: 27L1A009, Total marks: 1
28
There are 5.8 × 10 free electrons per cubic metre of silver. If a silver wire of
diameter 3.00 mm carries a current of 1.50 A, find the magnitude of the drift velocity
of the free electrons in the wire. The magnitude of the charge of an electron is
1.60 × 10–19 C.
A. 5.72 × 10−6 m s−1
B. 2.29 × 10−5 m s−1
C. 4.57 × 10−5 m s−1
D. 1.83 × 10−4 m s−1
Answer: B
*Code: 27L1A010, Total marks: 1
Which of the following phenomena is/are due to the magnetic force on charged
particles?
(1) the development of Hall voltage across the semiconductor slice in a Hall probe
head of
a Hall probe
(2) the heating effect in a current-carrying wire
hot wires in
a toaster
(3) the gain in kinetic energies of charged particles in a particle accelerator
particle
accelerator
in CERN
A.
B.
C.
D.
(1) only
(3) only
(1) and (2) only
(2) and (3) only
Answer: A
*Code: 27L1A011, Total marks: 1
A charged particle is projected perpendicularly towards a uniform field of unknown
nature as shown.
uniform
field
charged
particle
parabolic path
If the particle moves in a parabolic path in the field, which of the following statements
are correct?
(1) There is a constant force acting on the particle.
(2) The field can be a uniform electric field.
(3) The field can be a uniform magnetic field.
A. (1) and (2) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)
Answer: A
*Code: 27L1A012, Total marks: 1
A charged particle undergoes a uniform circular motion in a uniform magnetic field.
Which of the following statements is/are correct?
(1) The velocity of the particle is always perpendicular to the field.
(2) Work is done on the particle by the field.
(3) The period of the motion is directly proportional to the speed of the particle.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
Answer: A
*Code: 27L1A013, Total marks: 1
A particle of charge +Q is projected into a uniform magnetic field B perpendicularly
at speed v. The particle moves along a semicircular path and leaves the field as shown.
If another particle of the same mass but a charge of  Q 2 follows the same path in the
field, what is the speed of this particle?
A. v 2
B. v
C.
D.
2v
4v
Answer: A
*Code: 27L1B001, Total marks: 2
The figure below shows the paths of two charged particles A and B in a uniform
magnetic field.
A
B
uniform magnetic
field
Suppose particles A and B have the same mass and travel at the same speed. Compare
the quantities and the signs of the charges carried by the two particles.
(2 marks)
Answer:
Particle A is positively charged (1A) whereas particle B is negatively charged. The
quantity of charges carried by particles A is larger than that carried by particle B (1A).
*Code: 27L1B002, Total marks: 4
The figure below shows the path of an electron beam in a uniform magnetic field
ABCD.
(a) State the direction of the magnetic field.
(b) Draw the traces in the magnetic field if
(i) the magnetic field strength is increased;
(ii) the electron beam is replaced by a beam of positive ions.
(1 mark)
(1 mark)
(2 marks)
Answer:
(a) The magnetic field is pointing into the paper.
(b) (i) The electron beam will deflect with a larger scale.
(1A)
(1A)
(ii) The beam of positive ions bends in an opposite direction (1A) with a smaller
scale (1A).
*Code: 27L1B003, Total marks: 5
Three electrons X, Y and Z are moving in a uniform magnetic field at the same speed v
= 3.60 × 105 m s−1 as shown. The charge of electron is −1.60 × 10−19 C and the
magnitude of the magnetic field is 0.75 T.
X
60°
Z
Y
y
x
Find the magnitudes and directions of the magnetic forces acting on the electrons.
(5 marks)
Answer:
Consider electron X.
Its velocity makes an angle of 90° with the magnetic field. Applying F  qvB sin  ,
the magnitude FX of the magnetic force on X is
(1A)
FX  1.60  10 19  3.60  10 5  0.75  sin 90  4.32  10 14 N
By Fleming’s left hand rule, the direction of the force points out of the plane of the
paper.
(1A)
Consider electron Y.
Its velocity makes an angle of 180° with the magnetic field. Thus, the magnetic force
FY on Y is zero.
(1A)
Consider electron Z.
Its velocity makes an angle of (90° + 60°) = 150° with the magnetic field. Applying
F  qvB sin  , the magnitude FZ of the magnetic force on Z is
FZ  1.60  10 19  3.60  10 5  0.75  sin 150  2.16  10 14 N
(1A)
By Fleming’s left hand rule, the direction of the force points out of the plane of the
paper.
(1A)

 


 

*Code: 27L1B004, Total marks: 6
5 cm
to power
supply
h = 0.5 mm
to power
supply
d =0.5 cm
l = 1cm
(magnified)
The figure on the left shows the dimensions of the semiconductor slice in a Hall
probe. It is used to measure the magnitude of the magnetic field between the poles of
the strong magnet on the right. The charge of each charge carrier in the slice is
1.60 × 10−19 C.
(a) How would you place the probe in the field with the highest sensitivity? Sketch
your answer in the following figure.
(2 marks)
(b) The largest Hall voltage measured is 75.0 μV and the magnitude of the drift
velocity of the charge carriers in the slice is 3.50 × 10−2 m s−1. Find the
magnitude of the magnetic field measured by the probe.
(2 marks)
(c) The current flowing through the slice is 0.7 mA. Find the charge carrier density
in the slice.
(2 marks)
Answer:
(a)
to power
supply
h
l
d
to power
supply
(1A for correct orientation of the slice + 1A for labels of dimensions)
(b) In the steady state, the electric force on a charge carrier balances the magnetic
force on it. We have
qvB  qE
qV
qvB  H
d
V
B H
vd
(1M + 1A)
6
75.0  10
3.50  10 2  0.5  10 2 
 0.42857
 0.429 T
BI
(c) Applying VH 
, we have
nhQ
BI
n
hQV H


0.42857   0.7  10 3 
0.5  10  1.60  10  75.0  10 
3
19
6
(1M + 1A)
 5.00  10 22 m 3
*Code: 27L1B005, Total marks: 6
Isotopes are atoms of an element having the same number of protons but different
numbers of neutrons. A nucleus of an isotope is projected into a uniform magnetic
field B perpendicularly at speed v. The nucleus moves along a semicircular path and
leaves the field as shown. The mass and charge of the nucleus is m and +Q
respectively.
(a) By considering the magnetic force on the nucleus, find the radius of the
semicircular path in terms of m, v, Q and B.
(2 marks)
(b) Briefly describe how the set up can be used to identify nuclei of different
isotopes of the same element. State the assumption you have made.
(3 marks)
(c) Another nucleus of a heavier isotope of the same element is projected into the
field at the same velocity. Sketch the path of this nucleus in the above figure.
(1 mark)
Answer:
(a) The magnetic force provides the centripetal force of the circular motion. We have
mv 2
 QvB
r
(1M + 1A)
mv
r
BQ
(b) Assume the nuclei are projected to the field at the same velocity (1A). The nuclei
will perform circular motion in the field and the radii depend on the mass and
mv
charge of the nuclei as shown by the equation r 
(1A). Since nuclei of
Bq
different isotopes of the same element only differ in their masses (1A). By
measuring the radius of the circular path, we can identify nuclei of different
isotopes.
(c)
path of a
heavier isotope
path of the
original isotope
(1A for a semicircular path of larger radius)