Download Format: For each problem you must draw a diagram! detailing the

Format: For each problem you must draw a diagram! detailing the situation. Zero point will be given for
a good answer without the proper derivation (intermediate steps). Write clearly and detail (very briefly)
the logic of the steps that you are using. If I cannot understand what you are doing, you will lose marks.
Problem 1 (4 points) Ampere’s Law 1
A current flows down a long cylindrical wire (shown below). Using Ampere’s Law (a) find the magnetic
field both inside (r < R) and outside (r > R) if the current is distributed uniformly inside the wire, (b) find
the magnetic field both inside (r < R) and outside (r > R) if all of the current flows only on the surface of
the wire.
*Problem 2 (3 points) Ampere’s Law 2
Two long coaxial solenoids each carry a current I =1A in opposite directions (shown below). The inner
solenoid has a radius 1m and 1000 turns per meter, the outer solenoid has a radius 2m and 500 turns
per meter. Find 𝐵􁈬⃗ (a) inside the inner solenoid, (b) between the two, and (c) outside both. Use the
superposition principle!
Problem 3 (2 points) Magnetic flux
A coil of resistance R = 1 Ω and sides of length a = 0.5m and b = 1m lies in a plane perpendicular to a
magnetic field of strength B=0.2T, as shown above. (a) What is the magnetic flux though the loop? (b)
What would be the flux if 𝐵􁈬⃗ makes an angle of 500 with respect to the z-axis?
Problem 4 (3 points) Faraday’s Law 1
Consider again the circuit shown in Problem 4, when the magnetic field is along the z-axis. Suppose that
the magnetic field is reduced at a uniform rate until it is entirely turned off after 100 μs, as shown
below. (a) What is the induced emf (ε) around the loop? (b) What is the induced current (magnitude and
direction)? (c) What is the induced current after t=100 μs if B remains zero?
Problem 5 (3 points) Faraday’s Law 2
In the circuit shown below, the bar is moving at a constant velocity 𝑣⃗ . There is a uniform magnetic field
𝐵􁈬⃗ pointing out of the page everywhere. The circuit has zero resistance except for the resistor R. (a)
What is the induced 𝜀 in the circuit? (b) How much power is dissipated in the resistor R? (c) What is the
force (magnitude and direction) exerted on the bar by the magnetic field?
Problem 6 (3 points) Alternating current generator
A rectangular loop of N turns of length a and width b is rotated with a frequency f in a uniform magnetic
field 𝐵􁈬⃗ directed into the page (see below). (a) Calculate the induced the induced emf that appears in
the loop (generator) as a function of time. (b) Design a loop (give dimensions) that will produce a peak
value of 220V when rotated at 60Hz in a 1T field.
Problem 7 (2 points) Eddy currents
A metal pendulum (shown below) is moving into a magnetic field. (a) What is the orientation of the
induced eddy currents? (b) What is the direction of the force on the pendulum that results from the
eddy currents?
Problem 8 (2 points) 4 Laws of Electricity and Magnetism
(a) Write down the 4 fundamental equations of electricity and magnetism (b) Explain in English (one
sentence per equation) what is the physical meaning of each equation?
Problem 9 (3 points) Self-inductance
(a) Using Faraday’s Law, derive the self-inductance per unit length of a long (ideal) solenoid with n turns
per unit length, and of radius R. (b) How much energy is stored in this solenoid (per unit length) if it is
carrying a current 𝐼? (you can use the formula from the book for part (b))