ELECTROMAGNETISM & RELATIVITY - Chapter 5, Exercise 1 Solution
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Induced EMF from a Decreasing Magnetic Field

PROBLEM
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A 50-turn coil has an area of 0.02 m^2. The magnetic field through
it, initially 0.6 T, drops to 0.1 T over 0.25 s. Calculate the
magnitude of the induced EMF.

SOLUTION
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Step 1: Find the change in magnetic flux.

    delta Phi = delta B x A
    delta B = 0.6 - 0.1 = 0.5 T
    delta Phi = 0.5 x 0.02
    delta Phi = 0.01 Wb

Step 2: Apply Faraday's law to find the EMF magnitude.

    epsilon = N (delta Phi / delta t)
    epsilon = 50 x (0.01 / 0.25)
    epsilon = 50 x 0.04
    epsilon = 2 V

ANSWER: The magnitude of the induced EMF is 2 V.

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WHY THIS WORKS AS AN ANSWER

Faraday's law only cares about the SIZE of the change in flux and how
quickly it happens - it makes no difference here that the field is
DECREASING rather than increasing, as it was in the chapter's own
worked example. The formula uses delta B (the magnitude of the
change), giving a positive flux change of 0.01 Wb regardless of
direction, and dividing by the 0.25 s over which it happens gives the
induced EMF's own magnitude directly. Lenz's law would separately
determine the actual DIRECTION of the induced current - here, it
would flow in whatever direction creates a magnetic field trying to
maintain (oppose the loss of) the original, now-shrinking field,
exactly the mirror image of the chapter's own rising-field example.