Electromagnetic Induction unit test
A test on this unit alone, marked as a percentage and a letter grade — for the test your class is actually sitting, rather than for May. Answer everything, then submit once: seeing the answer to question 3 before attempting question 4 makes the final percentage meaningless.
Why Lenz's law must hold
Motional emf
Faraday's law
Maxwell's equations qualitatively
RL circuit
Lenz's law
Magnetic flux
Energy in an RL circuit
LC oscillation
Inductance
Force opposing motion
Mutual inductance
Short answer 1. Define or explain: Determining induced current direction
3 ptsShort answer 2. Define or explain: Energy stored in an inductor
3 ptsShort answer 3. Define or explain: Applying Lenz's law
3 ptsShort answer 4. Define or explain: Displacement current
3 ptsFree response
8 ptsQUALITATIVE/QUANTITATIVE TRANSLATION (Question 4, 8 points). In Scenario 1, a square conducting loop of side s and total resistance R is fixed in the xy-plane in a uniform, time-varying external magnetic field, initially in the +z-direction, with z-component Bz = B0·cos(2πt/t1), where B0 and t1 are positive constants. For C: in Scenario 2, a new square loop of side 2s and total resistance 2R sits in the same field; the maximum induced currents in Scenarios 1 and 2 are I1 and I2.
A. Indicate whether the induced current I in the loop is clockwise, counterclockwise, or zero during 0 < t < t1/4 (viewed from the +z-axis), and justify without only manipulating equations.
B. Derive an expression for I as a function of t, in terms of s, R, B0, t1, t, and physical constants, as appropriate.
C. Indicate whether I2 is greater than, less than, or equal to I1, and briefly justify by referencing the expression derived in part B.