A coil of N turns is shaped like a circular loop with aradius R . The coil is pl

Question

A coil of N turns is shaped like a circular loop with aradius R. The coil is placed in a spatially uniformmagnetic field that is perpendicular to the face of the coil andhas a field strength given by

B = Boe-at

Derive an expression for the induced emf in the coil as a functionof time. (Your expression will include the variablesBo, a, R, and N.)

QuestionDetails:

A coil of N turns is shaped like a circular loop with aradius R. The coil is placed in a spatially uniformmagnetic field that is perpendicular to the face of the coil andhas a field strength given by

B = Boe-at

Derive an expression for the induced emf in the coil as a functionof time. (Your expression will include the variablesBo, a, R, and N.)

Explanation / Answer

E = - d / dt = - A dB / dt dB / dt = - B0 a e-at E = A  B0 a e-at = R2 B0 ae-at       (1 turn) E = N R2 B0 ae-at E = A  B0 a e-at = R2 B0 ae-at       (1 turn) E = N R2 B0 ae-at

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