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 Times 0.55m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 65 degree with respect to the normal to the plane of the loop. A) If the magnetic field decreases at a rate c 4.67 T/s, what is emf induced in the loop? If the magnetic field stays constant at its initial value of 2.1 T, what is the magnitude of the rate dA/dt at which the area should change so the that the average emf is the same as in part A?

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt    or NABW   or   NA dB/dt cos theta

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of amgnetic flux

a) emf = -n /t

= -1 (0.35x0.55) [(0 - 2.1) cos65 / 0.467 ]

= 0.366V

b) emf = n B cos65 (A / t)

=> 0.366 = 2.1(A / t)

so A / t = 0.8 / 1.57 = 0.174 m^2/s

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