A constant magnetic field passes through a single rectangular loop whose dimensi

Question

A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m by 0.55 m. The magnetic field has a magnitude of 2.5 T and is inclined at an angle of 65 degrees with respect to the normal to the plane of the loop. (a.) If the magnetic field decreases to zero in a time of 0.30 s, what is the magnitude of the average emf induced in the loop? b.) If instead the magnetic field remains constant at 2.5 T at the same angle, at what rate should the area change (?A /?t) so that the average emf has the same magnitude as in part (a.) Please solve step by step.

Explanation / Answer

A = 0.35*0.55 m^2, B1 = 2.5 T, theta =65 degrees, t = 0.3 s
B2 = 0

from faradays law
induced emf V = -d(phi)/dt
V = A*(B1 -B2)cos(theta)/t
V = 0.35*0.55*(2.5 -0)*cos(65)/0.3
V = 0.678 V
(b) V = B*cos(theta)*(DA/Dt)
0.678 = 2.5*cos(65)*(DA/Dt)
DA/Dt = 0.642 m^2/s

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