Question

# The plane of a rectangular coil, 5.0-cm by 8.0-cm, is perpendicular to the direction of a magnetic field "B". If the coil has 75 turns and a total resistance of 8.0 Ohms, at what rate must the magnitude of "B" change to induce a current of 0.10 amps in the windings of the coil?

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The plane of a rectangular coil, 5.0-cm by 8.0-cm, is perpendicular to the direction of a magnetic field "B". If the coil has 75 turns and a total resistance of 8.0 Ohms, at what rate must the magnitude of "B" change to induce a current of 0.10 amps in the windings of the coil?

2021-02-16

Area of the recangualr ciol = A:
$$\displaystyle{A}={5}{c}{m}\times{8}{c}{m}=\frac{{40}}{{10000}}={0.004}{m}^{{{2}}}$$
Let , the rate of change of magnetic field is : d B / dt = ?
current = I = 0.1 A
resitence = R = 8 ohms
thus, amount of induced emf in would be
$$\displaystyle{e}={I}{R}={0.1}\times{8}={0.8}{v}{o}{<}$$
No. of turns of the coil = N = 75 turns
It is known by the formula for
Induced emf is :
e = A N dB / dt
thus, d B / dt = e / N A
$$\displaystyle=\frac{{0.8}}{{75}}\times{0.004}$$
= 0.8 / 0. 3
= 2.7 T /s (2.666666667)