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AL-LQ-E&M / p.1
1.
(89-IIB-10)
The figure shows an aluminium plate with a current of 50 mA passing through it.
(a)
29
(i)
Calculate the average drift velocity of the conducting electrons, given that there are 10
(ii)
conducting electrons per m of aluminium and the charge of an electron is 1.6  10 C. (2 marks)
A uniform magnetic field of 1.5 T is now applied normally downwards to the plate and covers the whole
19
3
surface area. Mark on the above figure the direction of the force experienced by each electron and
calculate its magnitude.
(3 marks)
(b) It is found that an electric field and a p.d. (the Hall p.d.) are created across the plate and soon attain maximum
values. Explain why this happens.
(4 marks)
(c) An experiment is being set up to demonstrate the Hall voltage and it is decided to use a gemanium slice. The
circuit diagram for the experiment is shown in the following figure.
(i)
Explain why a germanium slice was chosen in this experiment instead of an aluminium plate.
(2
marks)
(ii)
After switch S has been closed, a small p.d. is found to exist between X and Y even in the absence of a
magnetic field. Explain why this is so. How would you arrange X and Y to be at the same potential?
(3
marks)
(d) A uniform magnetic field of 0.2 T is now applied acting perpendicularly downwards into the plane of the paper,
covering the whole surface of the slice. If the reading of the millammeter is 1 mA, estimate the Hall voltage that
exists across the slice.
(the thickness fo the slice = 0.1 mm,
number of charge-carries per unit volume for germarium = 10
the charge on each carrier = 1.6  10
19
20
m 3 ,
C. )
(4 marks)
(e) Mention one practical application of the Hall effect.
2.
(90-IIB-10)
(1 mark)
AL-LQ-E&M / p.2
The figure shows a long uniformly-wound solenoid with a small brass disc mounted inside so that its plane is
perpendicular to the magnetic field inside the coil. The disc spins on an axle which lies along the axis of the solenoid,
which is connected in series with a d.c. power supply and a resistor of resistance R. One end of the resistor is
connected to the rim of the disc and the other is connected to the axle via a centre-zero galvanometer.
(a)
The solenoid, of length
l , has N turns and carries a current I. What is the magnetic flux density inside the
solenoid? (1 mark)
(b)
The radius of the brass disc is r and the radius of the axle is s. If the brass disc rotates at a rate of f
revolutions per second, obtain an expression for the e.m.f. generated between the axle and the rim of the disc.
(4 marks)
(c)
As the rate of rotation of the disc is increased, it is possible that the galvanometer deflection may change
direction. Explain why.
(d)
(2 marks)
When the galvanometer registers no deflection,
f  f 0 . Find an expression for the resistance of the resistor R.
(3 marks)
3.
(91-IIB-10)
(Given : magnetic field at the centre of a coil of N turns
B
 0 NI
2r
AL-LQ-E&M / p.3
permeability of vacuum
 0  4  10 7 Hm 1
acceleration due to gravity
g  10 ms 2 )
A student sets up the above apparatus to measure current. Coil X is a 100-turn circular coil of mean diameter 300
mm. Square coil Y, also of 100 turns, is pivoted at the centre of Coil X and is free to turn about a horizontal axis
AA , in the plane of coil X. When there is no current, the rider is adjusted to make the pointer horizontal.
Coils X and Y are connected in series. When a current I flows through the coils, the rider has to be moved 80 mm to
the right to restore the pointer to a horizontal position.
(a)
In the spaces provided, indicate the direction of the magnetic filed produced by coil X at its centre when a
current I flows in the direction shown. Determine the magnetic field B at the centre of X.
(b)
(2 marks)
In which direction should the current in Coil Y be flowing? Indicate the current direction and the
corresponding directions of the forces acting on the 4 sides of Coil Y in the diagram below.
(c)
(d)
4.
(3 marks)
If the mass of the rider is 40 mg and Coil Y is of side 30 mm, estimate the value of the current I, assuming that
the magnetic field due to coil X is uniform across the coil Y.
(4 marks)
What is the advantage of using this method to measure current?
(2 marks)
(95-I-4)
AL-LQ-E&M / p.4
A rectangular coil of length a, breadth b, mass m and total resistance R falls freely, with its plane vertical. It enters a
region of uniform magnetic field B normal to the plane containing the coil.
(a)
If it so happens that the coil falls at constant velocity v just as it enters the field region till it completely leaves
that region, sketch the variation of induced e.m.f. in the coil with time during falling.
(b)
Write an expression for the induced current I in terms of B, v, R and the dimensions of the coil just as the coil
enters the field region.
(c)
(2 marks)
The induced current causes a heating effect in the coil. Use the answer obtained in (b) to find an expression for
the total thermal energy generated in the falling process.
(3 marks)
(d)
Where does the electrical energy come from?
(1 mark)
(e)
(i)
Write an equation relating the forces acting on the coil when it falls with constant
velocity in the field region.
(ii)
(96-I-7)
(a)
(1 mark)
Hence or otherwise express the total thermal energy obtained in (c) in terms of the
mass and the dimension of the coil.
5.
(2 marks)
(2 marks)
AL-LQ-E&M / p.5
A coil and a retort stand are arranged as shown above. The coil is connected to a d.c. supply by a switch S.
When the switch is closed, the aluminium ring placed on top of the coil jumps up momentarily and falls back
afterwards.
(i)
Briefly explain the phenomenon.
(3 marks)
(ii)
What would be observed if the d.c. supply is replaced by an a.c. one? Suggest a practical use of this
experimental result.
(2 marks)
1
o
o
(iii) The heat capacity of the ring is 7.8 JK
and its temperature rises from 25 C to 40 C during the
first 50 s when the a.c. supply is on. Find the average rate of increase in internal energy of the ring.
(2
marks)
(b)
A centre-zero galvanometer A (full-scale deflection of 100  A) is connected in series with a resistor, R, and a
1.5 V cell as shown above. The pointer of A deflects to the left.
(i)
Give the order of magnitude of R for protecting A from overload.
(1 mark)
(ii)
The galvanometer is now connected to a coil as shown below. A student moves a bar magnet with
uniform speed towards the coil and the pointer of A deflects to the right.
(I)
(II)
Indicate on the above figure the direction of the induced current in the coil and the poles of the
magnet.
(2 marks)
Where does the electrical energy in the circuit come from?
(1 mark)
(III) Suggest THREE ways to increase the deflection of A.
6.
(96-I-8)
(2 marks)
AL-LQ-E&M / p.6
The figure shows a simple current balance. A flat solenoid is connected to a horizontal rectangular copper loop
ABCD, such that the same current can pass through them as shown. The loop is pivoted on the axis XY which is
mid-way between AB and CD, with CD inside the solenoid and perpendicular to the axis of the solenoid. When a
4
current, I, flows through the solenoid and the loop, a rider of mass 10 kg has to be placed on AB to restore
equilibrium. The length, l, and the number of turns, N, of the solenoid are 50 cm and 600 respectively. The length of
CD is 20 cm.
(Permeability of free space
 o  4  10 7 Hm 1 )
(a)
Indicate on the above figure the direction of the magnetic field inside the solenoid.
(b)
(i)
 o NI
l
If the magnetic field strength inside the solenoid can be calculated by the formula
, find, in terms of I, the force acting on arm CD.
(ii)
(1 mark)
Hence deduce the value of I.
(2 marks)
(2 marks)
(c)
State and explain one precaution of the experiment.
(2 marks)
(d)
Is this current balance useful for measuring a.c. as well? Explain briefly.
(2 marks)
(e)
The solenoid is not infinitely long. What effects does this have on the value of I obtained in (b)? Explain briefly.
(2 marks)
7.
(98-I-7)
A solenoid of diameter 0.05m and length 0.45m has 100 turns of wire. A rectangular coil, of dimensions
AL-LQ-E&M / p.7
0.01 m x 0.01 m and negligible resistance, is connected by a pair of twisted wires to a resistor of resistance 100  .
The coil is placed inside the solenoid as shown below. The axis of the solenoid is perpendicular to the plane of the
coil. The current in the solenoid
I s varies with time t as shown. (Given : permeability of free space = 4 x 10 7
H m 1 )
(a)
If the induced current
I c in the coil is 0.01 A in the first 0.04 s,
(i)
find the maximum current Imax through the solenoid;
(4 marks)
(ii)
state TWO assumptions in your calculation;
(2 marks)
(iii) complete the graph of the induced current
I c in the coil from t = 0.04 s to t = 0.1 s.
(b)
What is the purpose of twisting the connecting wires?
(c)
If an ideal diode is connected in series with the coil and the 100  resistor so that there is no
(2 marks)
(1 mark)
current flowing in the resistor after t = 0.04 s, find (i) the maximum induced current in the coil, and (ii) the
maximum voltage drop across the diode from t = 0 s to t = 0.1 s.
8.
(2 marks)
(99-I-3)
A proton of mass m and charge q is accelerated from rest through a potential difference Vo and enters
perpendicularly through a small hole H on a screen S into a region with a uniform magnetic field B pointing into the
paper as shown below.
AL-LQ-E&M / p.8
(a)
Sketch the path of the proton in the above figure. Indicate the magnet force acting on the proton at an
arbitrary point on the path.
(b)
(i)
Derive an expression for the distance d from the hole H to the point where the proton hits
the screen. Find this distance for the proton if m = 1.67  10
Vo = 1000 V and B = 0.05 T.
(ii)
27
kg, q = 1.6  10
19
C,
(4 marks)
Calculate the time the proton spends in the magnet field (i.e. the time between leaving H and hitting
the screen).
(c)
(2 marks)
(3 marks)
The proton is now replaced by an unknown nucleus X whose charge is double that of a proton. Nucleus X hits
the screen at a distance of 0.26 m from H. Compare this with your result in (b)(i), and determine what X is.
marks)
9.
(00-I-7)
(a)
You are a member of a project group. Your group has planned a project to investigate the magnetic field
pattern around two parallel wires carrying currents in opposite directions. The project would include measuring and
comparing the field strength at different points around the two wires.
(3
AL-LQ-E&M / p.9
Figure (a)
(i)
A steady d.c. current is passed through the wires. Sketch in the space below the magnetic field pattern around the
two wires.
(2 marks)
Figure (b)
(ii)
With reference to Figure (c), if the current flowing through both wires is 5 A and the separation between them is
0.05 m, predict the magnitude of the magnetic field strength due to these two wires at point X, which is 0.02 m
from wire Q. (The diameters of the wires are negligible.)
Given : permeability of free space = 4  10 Hm-1
7
(2 marks)
Figure (c)
(iii)
Name the apparatus that you would use to measure the magnetic field in this experiment.
(1
mark)
(b)
Your group then submits the plan to the teacher. However, the teacher disagrees with the use of d.c. in this experiment and
he points out that the measuring apparatus available in the school laboratory is not sensitive enough to measure even the
earth’s magnetic field, which is about 50 T . He further suggests that since the plan is to compare the magnetic field
strength at different positions, absolute measurement of field strength is not necessary.
(i)
Suggest TWO reasons why the teacher disagrees with the use of d.c. in this experiment. (2 marks)
(ii)
Your group then decides to investigate the magnetic field pattern around two parallel current-carrying wires by
using a modified experiment. The set-up is shown in Figure (d). With the time base of the CRO switched off, a
vertical trace is observed on the screen of the CRO.
Figure (d)
(I)
(II)
Explain what is represented by the length of the trace observed on the CRO and state TWO advantages of
this modified experiment.
(3 marks)
State TWO necessary precautions for carrying out the experiment.
(2 marks)
AL-LQ-E&M / p.10
10.
(00-I-8)
(a)
Figure (a)
Figure (a) illustrates a thought experiment. A metal bar XY of length l is pulled through a uniform magnetic field B with a
velocity v. The direction of the velocity is perpendicular to the bar and they are both perpendicular to the magnetic field.
(i)
Draw on Figure (a) all the forces acting on the positive charge  Q in the bar. Label the forces.
(1
mark)
(ii)
Describe the movement of the charges in the bar and show that the e.m.f. induced across the ends XY is given by
  Blv .
(b)
(3 marks)
In 1996 astronauts on the space shuttle Columbia performed an experiment to test an idea for generating electricity in the
upper ionosphere. In the ionosphere, the ultraviolet radiation from the Sun or other radiations causes the air particles to
undergo ionization, and they tend to remain ionized as the chance of recombination is small. Once in orbit, Columbia
released a satellite attached to it by a 20 km long conducting cable. With the satellite vertically above the shuttle, the two
moved together around the earth above the equator.
Figure (b)
Given :
Magnetic field strength in the orbital region = 30  10
6
T
Orbital position of the shuttle = 6.8  10 m from the center of the earth
6
(i)
Mean radius of the earth = 6.4  10 m
Calculate the orbital speed of the shuttle at the orbital position.
(ii)
Estimate the e.m.f. induced across the cable. State the assumption(s) that you have made in the calculation.
6
(3 marks)
(3
marks)
(iii)
The experiment was in fact successful and a steady current was detected in the cable. Indicate the direction of the
current in the cable and explain why a current can be sustained.
11.
(3 marks)
(01-IA-4)
Figure 4.1 shows a solenoid of diameter 5.0cm. The solenoid has 1.0  10 turns and it carries a current of 60 mA. (Given:
3
7
permeability of free space = 4  10 Hm-1)
AL-LQ-E&M / p.11
Figure 4.1
(a) (i) Calculate the magnetic field strength at the center O of the solenoid. Justify the major assumption you made in the
calculation.
(ii) Calculate the magnetic flux linkage through the solenoid. Hence or otherwise find the inductance of the solenoid.
(Assume that the flux leakage of the solenoid is negligible.)
(b) The solenoid is now connected with a resistor R0 and a 3V battery as shown in Figure 4.2. When switch is opened the
variation of the current I through R0 with time t for the first 30μs is as shown.
Figure 4.2
According to the textbooks, the current would decrease exponentially as I  I 0 e
 Rt
L
, where R and L are the resistance and
inductance of the solenoid respectively. Assume that the resistance of R0is much smaller than R. (Given: e-x can be
approximated to 1-x for small x)
(i) Explain why the graph in Figure 4.2 appears to be a straight line.
(ii) Find the experimental values of R and L.
(iii) Account for the difference between the experimental value of L in (b)(ii) and its theoretical value in (a)(ii).
12.
(01-IA-5)
A simple electric motor has a rectangular coil of 120 turns, each of area 0.002m2, and of total resistance 0.8Ω. It is connected to
a 12V d.c. supply of negligible internal resistance. The strength of the uniform magnetic field in the region of the coil is 0.5T.
Figure 5.1 shows the variation of current with time t when the motor is switched on.
AL-LQ-E&M / p.12
Figure 5.1
(a)
(i)
Estimate the maximum value of the current I max.
(ii)
When the motor is switched on, the current is so large that it may burn out the coil. Explain how this can be
avoided.
(b)
(c)
13.
Explain why the current
(i)
does not rise immediately to its maximum value;
(ii)
Drops gradually from P to Q and becomes steady along QC.
(i)
What is the maximum torque acting on the coil due to the current when it is rotating at constant speed?
(ii)
For the motor running at constant speed, calculate
(I)
the back e.m.f. developed across the coil;
(II)
its efficiency in converting electrical power to mechanical power.
(03-IIB-4)
Figure 4.1 shows a circular coil of 100 turns and radius 5 cm pivoted by two smooth vertical bearings. It is placed in a region
with a uniform magnetic field of 0.1 T. The ends of the coil are joined together, the coil’s total resistance is 10  .
AL-LQ-E&M / p.13
uniform magnetic field
Figure 4.1
(a)
The coil is turned through 90 by an external force until its plane is perpendicular to the magnetic field.
(i)
Would the coil resist turned? Explain briefly.
(2 marks)
(ii)
If the coil is released from rest at the new position described above, would it move back to its original position?
Explain briefly.
(b)
(2 marks)
The coil is now fixed with its plane perpendicular to the magnetic field. The flux density of the field is increased at a
uniform rate of 0.3 T s
-1
in the first 5 s. It is then kept constant for another 5 s and is finally reduced at a uniform rate
-1
of 0.4 T s to zero.
(i) Write down an expression to describe the relationship between the magnitude of the flux density and time in the first
(ii)
5 s.
(1 mark)
Find the magnitude of the current induced in the coil in the first 5 s.
(3 marks)
(iii) Sketch a graph to show the variation of the current I induced in the coil from time t = 0 s to the time when the flux
density of the magnetic field becomes zero.
(3 marks)
I/A
0
14.
t/s
(04-IB-7)
Figure 7.1 shows an earth leakage circuit breaker (漏電斷路器) installed in a domestic circuit. The live and the neutral wires
pass through the center of a soft iron ring of mean radius 1cm. A 100-turn coil C with cross-section area 0.8cm2 is wound on the
rim of the ring. In case of an earth leakage in the domestic circuit such that the currents flowing in the neutral and live wires
differ by a value of 0.5A, the relay switch S of this device will open so as to switch off the main supply. The relay switch has to
AL-LQ-E&M / p.14
be reset mechanically in order to resume the supply.
Figu
re
7.1
(a)
(i)
Expl
ain
the
work
ing principle of the circuit breaker when there is a leakage of current from the load to the ground. (3 marks)
(ii)
(b)
Would the circuit breaker respond if a leakage to the ground occurs at P? Explain. (1 mark)
Suppose there is a leakage of current of 0.5A from the load to the ground.
(i)
It is known that the flux density of the magnetic field due to a current-carrying conductor will be 1500 times
larger in the presence of soft iron. Calculate the magnetic flux density B through coil C. (Given: permeability of
free space o=4p x 10-7 Hm-1) (3 marks)
(ii)
If the leakage develops steadily from 0A to 0.5A within a time interval of 0.03s, determine the e.m.f. induced in
the coil C. (Neglect the inductance of the solenoid.) (2 marks)
(c)
Electrical appliances are usually equipped with fuses. What would happen to the fuse and the earth leakage circuit breaker
if short circuit occurs between live and neutral in an appliance? Explain. (4 marks)
15.
(04-IB-8)
Figure 8.1 shows the apparatus using crossed magnetic and electric fields to measure the charge-to-mass ratio of electron. The
cathode-ray tube has a cathode C and an anode A with a horizontal collimating slit, from which the electrons emerge in a narrow
beam.
Figure 8.1
(a)
Describe how electrons are emitted from the cathode.
(b)
The Helmholtz coils, X1 and X2 are to provide a uniform magnetic field over some distance around the common axis
midway between the two. The e.h.t. is set at voltage V and a direct current I flows round the Helmholtz coils.
i.
State the direction of the magnetic field if the current flows round each coil in a clockwise direction. Suggest a
piece of apparatus for measuring the flux density of the magnetic field due to the Helmholtz coils.
ii.
Sketch and describe the trial of the electron beam between the defecting plates Y1 and Y2 if each of the
following changes is made independently:
(c)
(1)
Both Y1 and Y2 are connected to the positive terminal of the e.h.t. (2 marks)
(2)
The current in the Helmholtz coils is switched off.
The helmholtz coils, each of diameter 30cm, are connected in series to a d.c. power supply. The coils are parallel
AL-LQ-E&M / p.15
and 15cm apart. Each coil has 130 turns. The flux density B of the magnetic field midway between the coils near the
axis is given by
where
I is the current through the Helmholtz coils
N is the number of turns on each coil
A is the radius of the coils
0 =4 x 10-7 Hm-1
The e.h.t. is now set at 3kV and a direct current of 1.6A flows round the Helmholtz coils. The electron beam, which
is perpendicular to both the magnetic field and the electric field, emerges from between the deflection plates Y1 and
Y2 without deflection.
(i) Calculate the flux density B of the magnetic field between the coils near the axis. (2 marks)
(ii) If the separation between Y1 and Y2 is d, derive an expression for the charge-to-mass ratio of electron in turns of
B, V and d. Calculate the measured charge-to-mass ratio if d is 0.07m.
(iii) The accepted value of the chrge-to-mass ratio of electron is 1.76 x 1011 C kg-1. Suggest a cause that may lead to
the discrepancy between the accepted value and the experimental value obtained in (c)(ii).