# Electrodynamics Questions and Answers

Practice Electrodynamics Questions and Answers

## Electrodynamics Questions and Answers

Q1. One voltmeter of the range (0-200 millivolts) is connected across two rails, which are separated from each other as well as from the ground. When a train runs over these rails at a speed of 180 km/hour, then what will be the reading of the voltmeter? It is given that the vertical component of the earth’s magnetic field is 0.2 × 10 Weber/m2 and the rails are separated by a distance of 1 meter

• (a) 2 millivolts
• (b) 20 millivolts
• (c) 1 millivolts
• (d) 10 millivolts

Q2. A small loop of wire of area A 0.01 m2 ,N = 40 turns and resistance R = 20Ω is initially kept in a uniform magnetic field B in such a way that the field is normal to the plane of the loop. When it is pulled out of the magnetic field, a total charge of Q = 2 × 10-5 C flows through the coil. The magnitude of the field B is:

• (a) 1 × 10-3 T
• (b) 4 × 10-3 T
• (c) zero
• (d) Unobtainable as the data is insufficient

Q3. A conducting circular loop od wire is placed in a uniform magnetic field B 0.02 T with its plane perpendicular to the field. If the radius of the loop starts shrinking at a constant rate of 1.0 mm s-1, the induced e.m.f. on the loop at an instant when its radius is 2 cm is

• (a) 5 μ V
• (b) 5 m V
• (c) 2.5 m V
• (d) 2.5 μ V

Q4. Consider a small bar magnet under going simple harmonic motion (SHM) along the x-axis. A coil whose plane is perpendicular to the x-axis is placed Such that the magnet passes in and out of it during its motion. Which one of the following statements is correct? Neglect damping effects.

• (a) Induced e.m.f. is minimum when the center of the bar magnet crosses the coil
• (b) The frequency of the induced current in the coil is half of the frequency of the SHM
• (c) Induced e.m.f. in the coil will not change with the velocity of the magnet
• (d) The sign of the e.m.f. depends on the pole (N or S) face of the magnet which enters into the coil

Q5. A uniform magnetic field B is perpendicular to the plane of a circular wire loop of radius R. The magnitude of the field varies with time according to B = Bo exp(-t/τ) ,where Bo and τ are constants. The time dependence of the induced e.m.f. in the loop is

• (a) exp(-t22)
• (b) 1 + exp(-t22)
• (c) 1 – exp(-t/τ)
• (d) – exp(-t/τ)

Q6. A circular conducting ring of radius R rotates with constant angular velocity ω about its diameter placed along the x-axis. A uniform magnetic field B is applied along they-axis. If at time t=0 the ring is entirely in the xy-plane, the emf induced in the ring at time t>0 is

• (a) Bω2πR2t
• (b) Bω2πR2 tan(ωt)
• (c) Bω2πR2 sin(ωt)
• (d) Bω2πR2 cos(ωt)

Q7. Self inductance per unit length of a long solenoid of radius R with n tums per unit length is:

• (a) μoπR2n2
• (b) 2μoπR2n
• (c) 2μoπR2n2
• (d) μoπR2n

Q8. A metallic ring of area 1 cm2 and resistance 10Ω is placed in a perpendicular time varying magnetic field which has the following form:

B(t) = 2e-0.5tcos(2πt)

Where B is in Tesla and t is in seconds. The net charge that flows past any point in the ring from t=0 to t = ∞ is

• (a) 1 μC
• (b) 3 μC
• (c) 5 μC
• (d) 20 μC

Q9. A circular conducting loop of radius 2cm and Resistance1Ω lies in xy-plane. A constant magnetic field (B) of 1T applied along z-direction. If radius of loop is reduced from 2 cm to 1 cm, the total charge (Q) passes through given point in the loop is (in coulombs)

• (a) 0
• (b) 9.4 × 10-4
• (c) 9.4 × 10-2
• (d) 12.6 × 10-4

Q10. A long solenoid is embedded in a conducting medium and is insulated from the medium. If the current through the solenoid is increased at a constant rate, the induced current in the medium as a function of the radial distance r from the axis of the solenoid is proportional to

• (a) r2 inside the solenoid and 1/r outside
• (b) r2 inside the solenoid and 1/r2 outside
• (c) r2 inside the solenoid and 1/r2 outside
• (d) r2 inside the solenoid and 1/r outside

Q11. A spatially uniform time-dependent magnetic field is changing with time at the constant rate of 1 T/s. A unit positive charge is moved around a circle of radius R = 2m perpendicular to this field. The magnitude of the work done on the charge for one complete revolution is

• (a) 0
• (b) 2 J
• (c) 6.28 J
• (d) 12.56 J

Q12. Consider a solenoid of radius R with n turns per unit length, in which a time dependent current
I = Io sin ωt (where ωR/c << 1) flows. The magnitude of the electric field at a perpendicular distance r<R from the axis of symmetry of the solenoid, is:

• (a) 0
• (b) 1/2r ωμonIoR2 cos ωt
• (c) 1/2 ωμonIor sin ωt
• (d) 1/2 ωμonIor cos ωt

Q13. Which of the following proposed space-time dependent electric fields in vacuum is/are allowed by the equations of electromagnetic theory?

(I) Ex = E1 sin(kz-ωt) , Ey = E2 sin(kz-ωt) , Ez = 0
(II) Ex = E1 sin(kz-ωt) , Ey = 2E2 sin(kz-ωt) , Ez = 0
(III) Ex = E1 sin(kz-ωt) , Ey = 0 , Ez = E2 sin(kz-ωt)

(In the above E1 and E2 are real constants)

• (a) I and II, but not III
• (b) II and III, but not I
• (c) I and II, but not III
• (d) I only

Q14. At ‘equilibrium there can not be any free charge inside a metal. However, if you forcibly put charge in the interior then it takes some finite time to “disappear’ i.e, move to the surface. If the conductivity, σ , of a metal is 106 (Ωm)-1 and the dielectric constant εo = 8.85 × 10-12 Farad/m, this time will be approximately:

• (a) 10-5 sec
• (b) 10-11 sec
• (c) 10-9 sec
• (d) 10-17 sec

Q15. The skin depth of a metal is independent on the conductivity (σ) of the metal and the angular frequency ω of the incident field. For a metal of high conductivity, which of the following relations is correct ? (Assume that σ >> εω1 where ε is the electrical permittivity of the medium).

• (a) d ∝ √(σ/ω)
• (b) d ∝ √(1/σω)
• (c) d ∝ √(σω)
• (d) d ∝ √(ω/σ)

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