Magnetic field due to currentHard

Question

Inside a long cylindrical solenoid of radius R has a magnetic field exists which that is approximately uniform in space but varies with time as B = B0–βt, where B0 and  βare positive numbers. B points out of the paper at t = 0 in an end-on view of the solenoid as shown below. The magnitude and direction of the electric field at a radial distance 2R from the axis of the  solenoid is :

Options

A.

Rβ/4, counterclockwise

B.

Rβ/4, clockwise
 

C.

Rβ/2, counterclockwise
 

D.

Rβ/2, clockwise
 

Solution

CCW path at r = 2R gives 2π(2R)E = –(d/dt)[(B0 – βt)(πR2)]   ⇒E = Rβ/4 ; CCW
opposes the loss of B out of the paper just as would be the case if a real wire were there with E in the direction of I.

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