Figure shows a closed loop of wire that consists of a pair of equal semicircles, of radius 3.7 cm, lying in mutually perpendicular planes.The loop was formed by folding a flat circular loop along a diameter until the two halves became perpendicular to each other. A uniform magnetic field B of magnitude 76 mT is directed perpendicular to the fold diameter and makes equal angles (of 45°) with the planes of the semicircles. The magnetic field is reduced to zero at a uniform rate during a time interval of 4.5 ms. During this interval, what are the (a) magnitude and (b) direction (clockwise or counterclockwise when viewed along the direction of B) of the emf induced in the loop?

Respuesta :

(a) Magnitude of the average emf induced in the loop is 0.20 mV.

(b) direction is perpendicular to the field.

Average emf induced in the circular loop is given by;-

The magnitude of average emf induced in the loop is calculated as follows are;

emf = NA(B₁ - B₂)/t

by using the formula of the induced emf we calculate the average emf.

A = area of the loop

N =number of turns

B1 = initial magnetic field

B2 = final magnetic field

t=time

A = πr² = π(0.37)²

= 5.027 x 10⁻³ m²

emf = (1)(5.027 x 10⁻³)(0.45 - 0.37)/7.6

emf = 2.01 x 10⁻⁴ V

emf = 0.201 mV

Therefore,  magnitude of the average emf is induced in the loop = 0.20 mV.

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