Question

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003 10.0 points The plane of a rectangular coil, 4.8 cm by 10.1 cm, is perpendicular to the direction of a uniform magnetic fheld B

Answer 1

Start with Faraday's Law for a coil of N turns:

ℰ = -N dΦ/dt

where:
ℰ is the induced emf,
Φ is the magnetic flux through the area of the coil (this is usually written with subscript B), and
t is time

In the case of a uniform magnetic field (B) perpendicular to the plain of the coil:

Φ = BA

where A = (0.048 m * 0.101 m) is the area of the coil.

Combine those two equations:

ℰ = -N A dB/dt

(A is pulled out of the derivative because it is constant over time.)

For a coil of resistance R, the induced current is:

i = ℰ/R

i = -(N A / R) * dB/dt

The question asks you to find the rate of change of B, which is dB/dt

dB/dt = - iR/(NA)

Now just plug in your numbers:

dB/dt = -(0.08 A)(7 Ω)/(118 * (0.048 m * 0.101 m))

dB/dt = 0.9789 T/s