An N-turn circular wire coil of radius r lies in the xy-plane, as shown in the f

Question

An N-turn circular wire coil of radius r lies in the xy-plane, as shown in the figure below. A uniform magnetic field is turned on, increasing steadily from 0 to B0 in the negative z-direction in t seconds. (Use any variable or symbol stated above along with the following as necessary: R and pi.) Find a symbolic expression for the emf, epsilon, induced in the coil in terms of the variables given. Looking down at the xy-plane from the positive z-axis, is the direction of the induced current clockwise or counterclockwise? If each loop has resistance R, find an expression for the magnitude of the induced current, I.

Explanation / Answer

flux = B*A

emf = d(flux)/dt = dB/dt*area

= -B0/t *pie*r^2

Direction is clockwise

If resistance is R

then current I = V/R

I = (B0/t*pie*r^2 )/R

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