Question

The magnetic induction at the centre o in the figure shown is
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Answer 1

Explanation:

The resultant magnetic field at O will be the sum of the magnetic fields due to the current in the two semicircles, and we can use the expression for the magnetic field at the center of a current loop to find B.

The resultant magnetic field at point O is given as B = B1+B2

The magnetic field at the center of a current loop is B =

uoi/2πR

, where R is the radius of the loop.

The magnetic field at the center of half a current loop B =

1/2 *uoi/2πR = uoi/4πR

Therefore,

B1 = uoi/4πR1

B2 = - uoi/4πR2

So, B = B1+B2 = ( uoi/4πR1)- (uoi/4πR2)

That is,

(uoi/4π)*(1/R1- 1/R2)

ANSWER = (uoi/4π)*(1/R1- 1/R2)