Where is dB/dt nonzero in the figure? Exploit the analogy between Faraday\'s law

Question

Where is dB/dt nonzero in the figure?

Exploit the analogy between Faraday's law & Ampere's law to sketch (qualitatively) the electric Field.

In 1831 Michael Faraday reported on a series of experiments, including three that (with some violence to history) can be characterized as follows: He pulled a loop of wire to the right through a magnetic field (Fig. 7.20a). A current flowed in the loop. He moved the magnet to the left, holding the loop still (Fig. 7.20b). Again, a current flowed in the loop. With both the loop and the magnet at rest (Fig. 7.20c), he changed the strength of the field (he used an electromagnet, and varied the current in the coil). Once again, current flowed in the loop.

Explanation / Answer

dB/dt is non zero only in the third part (c), where in the question its explicitely wriiten that the magnetic field is varied.

in part a and b, the magnetic field strength is kept constant. however, the magnetic flux = B. A(area) is changing in both of the two cases as the area is changing:

d(B.A)/dt= A dB/dt + B dA/dt...... since dA/dt is non zero ==> induced emf ==> current in the loop.

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