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Final Exam
Electricity and Magnetism PHY 204
Instructor: Dr. Anzar Khaliq
(Time Allowed: 3 hours)
You are provided with a formula sheet. No other formulas outside of that sheet
will be provided. Part A consists of MCQ’s. You must return it after 1 hour.
Overwriting / Cutting will result in a very nice big zero.
Part B contains numerical problems. There are six problems in total. Attempt all
questions. The best five will be selected.
Part A (weightage in %)
30
Part B (weightage in %)
70
Courage etBonne Chance!
1
Formula Sheet
Total marks of part A: 30
Time: 1 hour
Final Exam: Electricity and Magnetism
PART A
Name:
Roll no:
Attempt all questions. Circle the appropriate answer. For multiple parts, write down the
proper option in front of each part separately. No overwriting/ cutting allowed!
1. If the net flux through a gaussian surface is zero, the following four statements could
be true. Which of the statements must be true? [1]
(a) There are no charges inside the surface.
(b) The net charge inside the surface is zero.
(c) The electric field is zero everywhere on the surface.
(d) The number of electric field lines entering the surface equals the number leaving
the surface.
FIG. 1
2. Suppose a point charge is located at the center of a spherical surface. The electric
field at the surface of the sphere and the total flux through the sphere are determined.
Now the radius of the sphere is halved. What happens to the flux through the sphere
and the magnitude of the electric field at the surface of the sphere? [1]
(a) The flux and field both increase.
(b) The flux and field both decrease.
(c) The flux increases, and the field decreases.
(d) The flux decreases, and the field increases.
Date: 11 December, 2013
1
Total marks of part A: 30
Time: 1 hour
(e) The flux remains the same, and the field increases.
(f) The flux decreases, and the field remains the same.
3. Rank the magnitudes of the electric field at points A, B, and C shown in Fig 2.
[1]
(a) EA > EB > EC
(b) EA = EB > EC
(c) EA > EB > EC = 0.
(d) EA < EB < EC
(e) Both (a) and (c).
FIG. 3
FIG. 2
4. In the Fig 3, take q1 to be a negative source charge and q2 to be the test charge.
[2]
(i) If q2 is initially positive and is changed to a charge of the same magnitude but
negative, what happens to the potential at the position of q2 due to q1 ? (c)
(a) It increases
(b) It decreases
(c) It remains the same.
(ii) When q2 is changed from positive to negative, what happens to the potential energy
of the two charge system? Choose from the same possibilities. (a)
5. Two point charges q and 2q lie on the x-axis. Which region(s) on the x-axis include a
point where the electric field due to the two point charges is zero? [1]
(a) To the right of 2q
(b) between 2q and point P,
(c) between point P and q
(d) to the left of q,
(e) both (a) and (c)
(f) both (b) and (d).
FIG. 4
Date: 11 December, 2013
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Total marks of part A: 30
Time: 1 hour
6. Two solid metal spheres of different radii are far apart. The spheres are connected by
a fine metal wire. Some charge is placed on one of the spheres. After electrostatic
equilibrium is reached, the wire is removed. Which of these quantities will be the same
for the two spheres? [1]
(a) The charge on each sphere.
(b) The electric field inside each sphere, at the same distance from the centre of the
spheres.
(c) The electric field just outside the surface of each sphere.
(d) The electric potential at the surface of each sphere.
(e) Both (b) and (c).
(f) Both (b) and (d).
(g) Both (a) and (c).
7. A current-carrying ohmic metal wire has a cross-sectional area that gradually becomes
smaller from one end of the wire to the other. The current has the same value for each
section of the wire, so charge does not accumulate at any one point. [2]
(i) How does the drift speed vary along the wire as the area becomes smaller? (a)
(a) It increases
(b) It decreases
(c) It remains constant.
(ii) How does the resistance per unit length vary along the wire as the area becomes
smaller? Choose from the same possibilities. (a)
8. Is a circuit breaker wired [1]
(a) in series with the device it is protecting,
(b) in parallel,
(c) neither in series or in parallel
(d) is it impossible to tell?
9. Assume a device is designed to obtain a large potential difference by first charging a
bank of capacitors connected in parallel and then activating a switch arrangement that
in effect disconnects the capacitors from the charging source and from each other and
reconnects them all in a series arrangement. The group of charged capacitors is then
discharged in series. What is the maximum potential difference that can be obtained
in this manner by using ten capacitors each of 500 µF and a charging source of 800
V? [1]
(a) 80 kV
(b) 8 kV
(c) 2.5 kV
(e) 80 V
(f) 8 V
(g) 0.
Date: 11 December, 2013
(d) 800 V
3
Total marks of part A: 30
Time: 1 hour
10. Electron A is fired horizontally with speed 1 Mm/s into a region where a vertical
magnetic field exists. Electron B is fired along the same path with speed 2 Mm/s.
[2]
(i) Which electron has a larger magnetic force exerted on it?
(a) A does.
(b) B does.
(c) The forces have the same nonzero magnitude.
(d) The forces are both zero.
(ii) Which electron has a path that curves more sharply?
(a) A does.
(b) B does.
(c) The particles follow the same curved path.
(d) The particles continue to go straight.
11. In Fig 5, assume I1 = 2 A and I2 = 6 A. What is the relationship between the
magnitude F1 of the force exerted on wire 1 and the magnitude F2 of the force exerted
on wire 2? [1]
(a) F1 = 6F2
(b) F1 = 3F2
(c) F1 = F2
(d) F1 = F2 /3
(e) F1 = F2 /6
FIG. 5
12. The current in the long wire is decreasing. What is the direction of the current induced
in the conducting loop below the wire (see Fig 6)? [1]
FIG. 6
Date: 11 December, 2013
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Total marks of part A: 30
Time: 1 hour
(a) Counter-clockwise.
(b) Clockwise.
(c) CCW or CW depending on the shape of the loop.
(d) No current is induced.
13. (i) As the square coil of wire in Fig (7a) moves perpendicular to the field, is an external
force required to keep it moving with constant speed?[3] (b)
(a) Yes
(b) No.
(ii) Answer the same question for the bar in Fig (7b). (a)
(iii) Answer the same question for the bar in Fig (7c). (b)
(a)
(b)
(c)
FIG. 7
14. Two solenoidal coils, A and B, are wound using equal lengths of the same kind of wire.
The length of the axis of each coil is large compared with its diameter. The axial
length of coil A is twice as large as that of coil B, and coil A has twice as many turns
as coil B. What is the ratio of the inductance of coil A to that of coil B? [1]
(a) 8
(b) 4
Date: 11 December, 2013
(c) 2
(d) 1
(e) 1/2
(f) 1/4
(g) 1/8.
5
Total marks of part A: 30
Time: 1 hour
15. A capacitor is connected to the terminals of a variable frequency oscillator. The peak
voltage of the source is kept fixed while the frequency is increased. Which statement
is true? [1]
(a) The rms current through the capacitor increases.
(b) The rms current through the capacitor decreases.
(c) The phase relation between the current and the source voltage changes.
(d) The current stops flowing when the frequency change is large enough.
16. A student working with transmitting apparatus, wishes to adjust the electrodes to
generate electromagnetic waves with a frequency half as large as before. [2]
(i) How large should she make the effective capacitance of the pair of electrodes?
(a) 4 times larger than before
(b) 2 times larger than before.
(c) 1/2 as large as before
(d) 1/4 as large as before.
(e) None of these answers would have the desired effect.
(ii) After she makes the required adjustment, what will the wavelength of the transmitted wave be?
(a) 4 times larger than before
(b) 2 times larger than before.
(c) the same as before
(d) 1/2 as large as before.
(e) 1/4 as large as before
(f) None of these answers is necessarily true.
17. Assume you charge a comb by running it through your hair and then hold the comb
next to a bar magnet. Do the electric and magnetic fields produced constitute an
electromagnetic wave? [1]
(a) Yes they do, necessarily.
(b) Yes they do because charged particles are moving inside the bar magnet.
(c) They can, but only if the electric field of the comb and the magnetic field of the
magnet are perpendicular.
(d) They can, but only if both the comb and the magnet are moving.
(e) They can, if either the comb or the magnet or both are accelerating.
18. A small source radiates an electromagnetic wave with a single frequency into vacuum,
equally in all directions. [5]
(i) As the wave moves, does its frequency (c)
(a) increase,
Date: 11 December, 2013
(b) decrease,
(c) stay constant?
6
Total marks of part A: 30
Time: 1 hour
Answer the same question about
(ii) its wavelength, (c)
(iii) its speed, (c)
(iv) its intensity, (b)
(v) the amplitude of its electric field. (b)
19. A spherical interplanetary dust grain of radius 0.2 µm is at distance r1 from the Sun.
The gravitational force exerted by the Sun on the grain just balances the force due to
radiation pressure from the Suns light. [2]
(i) Assume the grain is moved to a distance 2r1 from the Sun and released. At this
location, what is the net force exerted on the grain? (c)
(a) toward the Sun.
(b) away from the Sun.
(c) zero.
(d) impossible to determine without knowing the mass of the grain.
(ii) Now assume the grain is moved back to its original location at r1 , compressed
so that it crystallizes into a sphere with significantly higher density, and released. In
this situation, what is the net force exerted on the grain? Choose from the same
possibilities. (a)
Date: 11 December, 2013
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Total marks of part B: 25
Time: 2 hours
Final Exam: Electricity and Magnetism
PART B
Attempt all questions. Best 5 questions will be selected.
1. A spherical cavity of radius 4.50 cm is at the center of a metal sphere of radius 18.0
cm. A point charge Q = 5.50 µC rests at the very center of the cavity, whereas the
metal conductor carries no net charge. Determine the electric field at a point,
(a) 3.00 cm from the center of the cavity, [2]
(b) 6.00 cm from the center of the cavity, [1]
(c) 30.0 cm from the center. [2]
2. The circuit in Fig 1 consists of two identical, parallel metal plates connected by identical metal springs to a 100 V battery. With the switch open, the plates are uncharged,
are separated by a distance d = 8.00 mm, and have a capacitance C = 2.00 µF. When
the switch is closed, the distance between the plates decreases by a factor of 0.500.
(a) How much charge collects on each plate? [2.5]
(b) What is the spring constant for each spring? [2.5]
Hint: Derive the relation for force exerted on each plate using F =
C=
Aε0
,
x
dU
dx
and capacitance
where x is the arbitrary plate separation.
FIG. 1
3. A wire is formed into the shape of two half circles connected by equal length straight
sections as shown in Fig 2. A current I flows in the circuit clockwise as shown.
Date: 11 December, 2013
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Total marks of part B: 25
Time: 2 hours
Determine
(a) the magnitude and direction of the magnetic field at the center, C, [3]
(b) and the magnetic dipole moment of the circuit. [2]
FIG. 2
4. In Fig 3, the rolling axle, 1.50 m long, is pushed along horizontal rails at a constant
speed v = 3.00 m/s. A resistor R = 0.400 Ω is connected to the rails at points a and b,
directly opposite each other. The wheels make good electrical contact with the rails,
so the axle, rails, and R form a closed loop circuit. The only significant resistance in
the circuit is R. A uniform magnetic field B = 0.0800 T is vertically downward.
(a) Find the induced current I in the resistor. [1.5]
(b) What horizontal force F is required to keep the axle rolling at constant speed?
[1.5]
(c) Which end of the resistor, a or b, is at the higher electric potential? [1]
(d) What If? After the axle rolls past the resistor, does the current in R reverse
direction? Explain your answer. [1]
FIG. 3
5. A radar transmitter contains an LC circuit oscillating at 1.00 × 1010 Hz.
(a) What capacitance resonates with a one-turn loop having an inductance of 400 pH
Date: 11 December, 2013
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Total marks of part B: 25
Time: 2 hours
at this frequency? [2]
(b) The capacitor has square, parallel plates separated by 1.00 mm of air. What should
the edge length of the plates be? [2]
(c) What is the common reactance of the loop and capacitor at resonance? [1]
6. A linearly polarized microwave of wavelength 1.50 cm is directed along the positive x
axis. The electric field vector has a maximum value of 175 V/m and vibrates in the
xy plane.
(a) Assuming the magnetic field component of the wave can be written in the form
B = Bmax sin(kx − ωt), give values for Bmax , k, and ω. Also, determine in which plane
the magnetic field vector vibrates. [2]
(b) Calculate the average value of the Poynting vector for this wave. [1]
(c) What radiation pressure would this wave exert if it were directed at normal incidence onto a perfectly reflecting sheet? [1]
(d) What acceleration would be imparted to a 500 g sheet (perfectly reflecting and at
normal incidence) with dimensions of 1.00 m × 0.750 m? [1]
Date: 11 December, 2013
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