Electricity and Magnetism for the Physics Olympiad — Practice

Question 1

A rod of length 0.5 m rotates at 10 rad/s about one end in a 0.2 T field. Find the emf.

Accepted Answer

emf = (1/2)(0.2)(10)(0.25) = 0.25 V.

Question 2

Does the period of a charged particle in a uniform magnetic field depend on its speed?

Accepted Answer

No. T = 2 pi m/(qB), independent of speed.

Question 3

A capacitor charged to V is connected in parallel with an identical uncharged one. Find the final energy compared with the initial.

Accepted Answer

Each ends at V/2, so the final energy is 2 x (1/2) C (V/2)^2 = CV^2/4, half of the initial CV^2/2.

Question 4

A charge q is a distance d from a grounded conducting plane. Find the force on it.

Accepted Answer

The image is -q at distance 2d, so the force is q^2/(4 pi epsilon0 (2d)^2), toward the plane.

Question 5

A cube has a resistor R on each edge. State the resistance between opposite corners.

Accepted Answer

5R/6.

Question 6

A rod of length l slides at constant speed v along rails of total resistance R in a field B. Show the mechanical power equals the electrical power.

Accepted Answer

emf = Blv, current I = Blv/R, force on the rod BIl = B^2 l^2 v/R. Mechanical power = Fv = B^2 l^2 v^2/R, equal to I^2 R.

Question 7

Find the field inside a uniformly charged solid sphere of radius R and charge Q at distance r from the centre.

Accepted Answer

The enclosed charge is Q r^3/R^3, so E = Q r/(4 pi epsilon0 R^3), rising linearly from the centre.

Question 8

What is the field inside a long solenoid with n turns per metre carrying current I?

Accepted Answer

B = mu0 n I.

Practice — Electricity and Magnetism for the Physics Olympiad