A circular wire loop with radius of 2.00m radius is perpendicular to a uniform f

Question

A circular wire loop with radius of 2.00m radius is perpendicular to a uniform field, with half the area of the loop in the field as shown in the figure below. The looo contains a 2 (omega sign) resistor. If the magnitude of the field varies with time according to B=0.0420t-0.870t^2, with B in teslas.

A. What is the magnetic flux through the loop at t=3.00s?

B. What is the magnitude of the emf induced in the resistor when t=3.00s? (Assume wire has no resistance)

C. What is the magnetude of the current in the wire when t=3.00s?

D. What is the power dissipated in the resistor when t=3.00s?

Explanation / Answer

a. flux = AB = 3.14 * 2* 2 * (0.042* 3- 0.870 * 9) = 96.76/2 =   48.38 Wb

b. emf e = A dB/dt

       = 3.14 *4 * (0.042 -5.22)/2 = 32.5 volts

c. i = e/R = 32.5/2 = 16.25 A

d. power = ei   = 32.5 *16.25 = 528 Watts

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