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/m ^{2} 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 m ^{2} ,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 = B _{o} exp(-t/τ) ,where B_{o} and τ are constants. The time dependence of the induced e.m.f. in the loop is**

*(a) exp(-t*^{2}/τ^{2})*(b) 1 + exp(-t*^{2}/τ^{2})*(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) Bω*^{2}πR^{2}t*(b) Bω*^{2}πR^{2}tan(ωt)*(c) Bω*^{2}πR^{2}sin(ωt)*(d) Bω*^{2}πR^{2}cos(ωt)

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

*(a) μ*_{o}πR^{2}n^{2}*(b) 2μ*_{o}πR^{2}n*(c) 2μ*_{o}πR^{2}n^{2}*(d) μ*_{o}πR^{2}n

**Q8. A metallic ring of area 1 cm ^{2} and resistance 10Ω is placed in a perpendicular time varying magnetic field which has the following form:**

**B(t) = 2e ^{-0.5t}cos(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) r*^{2}inside the solenoid and^{1}/_{r}outside*(b)**r*inside the solenoid and^{2}^{1}/_{r2}*outside**(c)**r*inside the solenoid and^{2}^{1}/_{r2}*outside**(d)**r*inside the solenoid and^{2}^{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 currentI = I _{o} 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}ωμ_{o}nI_{o}R^{2}cos ωt*(c)*^{1}/_{2}ωμ_{o}nI_{o}r sin ωt*(d)*^{1}/_{2}ωμ_{o}nI_{o}r 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) E _{x} = E_{1} sin(kz-ωt) , E_{y} = E_{2} sin(kz-ωt) , E_{z} = 0**

(II) E_{x} = E_{1} sin(kz-ωt) , E_{y} = 2E_{2} sin(kz-ωt) , E_{z} = 0

(III) E_{x} = E_{1} sin(kz-ωt) , E_{y} = 0 , E_{z} = E_{2} sin(kz-ωt)

**(In the above E _{1} and E_{2} 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 10 ^{6} (Ωm)^{-1} and the dielectric constant ε_{o} = 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 >> εω _{1} 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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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (c) | 06. | (d) | 11. | (d) |

02. | (a) | 07. | (a) | 12. | (d) |

03. | (d) | 08. | (d) | 13. | (a) |

04. | (a) | 09. | (b) | 14. | (d) |

05. | (d) | 10. | (d) | 15. | (b) |