Problem 1:

A solenoid is designed to store U_L = 0.10 J of energy when it carries a current of I = 450 mA.  The solenoid has a cross-sectional area of A = 5.0 cm² and a length l = 0.20m.  How many turns of wire must the solenoid have?

Problem 2:

Suppose that a very long coaxial line is divided into three regions
(i)  current I into the page for 0 < r < a
(ii)  current 0 for radius a < r < b
(iii)  current I out of the page for b < r < c.
Assume each conductor to have a uniform current density.  Find B for
(a)  r < a,
(b)  a < r < b,
(c)  b < r < c,
(d)  r > c.

Problem 3:

Two concentric spherical shells of radii a (inner) and b (outer) are separated by a material of conductivity s.  If they are maintained at a potential difference V, what current flows between them?  What is the resistance between the shells when b >> a?

Problem 4:

In the circuit shown below, all three voltmeters are ideal and identical.  Each resistor has the same given resistance R.  Voltage V is also given.  Find the reading of each voltmeter.

Problem 5:

A converging magnetic field is often used as a magnetic mirror.  Consider a symmetric converging field with ¶B_z/¶z = f(z).   Show that the radial component of B in cylindrical coordinates, namely B_r, where r = xi + yj is given by B_r = -(r/2)f(z).

Problem 6:

(a)  An aluminum wire has a resistance of 0.10 W.  If you draw this wire through a die, making it thinner and twice as long, what will be its new resistance?
(b)  Four copper wires of equal length are connected in series.  The cross sectional areas are 1 cm², 2 cm², 3 cm², and 5 cm².  A voltage of 120 V is applied to the arrangement.  What is the voltage across the 2 cm² wire in units of volt?

Problem 7:

A particle with mass M and charge q > 0 moves in a uniform magnetic field B and also in the field of another charge Q < 0 located at the origin.  At t = 0 the particle is at x = z = 0, y = a, and its velocity is v₀i.  For what B will the trajectory of the particle be a circle of radius a centered at the origin?