A 1000-turn loop of wire is connected to a 30.0 ohm resistor as shown in the fig

Question

A 1000-turn loop of wire is connected to a 30.0 ohm resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points into the paper and has a magnitude that varies in time as B=gt, where g=0.55 Tesla per second . Neglect the resistance of the wire.

If the magnitude of the potential difference between points a and b is 15.9 V, what is the radius of the loop?

A 1000-turn loop of wire is connected to a 30.0 ohm resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points into the paper and has a magnitude that varies in time as B=gt, where g=0.55 Tesla per second . Neglect the resistance of the wire. If the magnitude of the potential difference between points a and b is 15.9 V, what is the radius of the loop?

Explanation / Answer

here emf e = iR

so current i = emf/R

i = 15.9/30

i = 0.53 Amps

now also apply induced emf e = NAdB/dt

Area A = 15.9/(1000 * 0.55)

A = pi r^2 = 0.0289

r = 9.6 cm

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