A loop of wire in the shape of a rectangle rotates with a frequency of 284 rotation per minute in an applied magnetic field of magnitude 6 T. Assume the magnetic field is uniform. The area of the loop is A = 4 cm2 and the total resistance in the circuit is 9 Ω.(a) Find the maximum induced emf.(b) Find the maximum current through the bulb.

a) Magnitude of maximum emf induced = 0.0714 V = 71.4 mv

b) Maximum current through the bulb = 0.00793 A = 7.93 mA

Explanation:

a) The induced emf from Faraday's law of electromagnetic induction is related to angular velocity through

E = NABw sin wt

The maximum emf occurs when (sin wt) = 1

Maximum Emf = NABw

N = 1

A = 4 cm² = 0.0004 m²

B = 6 T

w = (284/60) × 2π = 29.75 rad/s

E(max) = 1×0.0004×6×29.75 = 0.0714 V = 71.4 mV

Note that: since we're after only the magnitude of the induced emf, the minus sign that indicates that the induced emf is 8n the direction opposite to the change in magnetic flux, is ignored for this question.

b) Maximum current through the bulb

E(max) = I(max) × R

R = 9 ohms

E(max) = 0.0714 V

I(max) = ?

0.0714 = I(max) × 9

I(max) = (0.0714/9) = 0.00793 A = 7.93 mA

Hope this Helps!!

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