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The figure shows a circular loop of radi...

The figure shows a circular loop of radius `a` with two long parallel wires `(numbered 1 and 2)` all in the plane of the paper . The distance of each wire from the centre of the loop is `d`. The loop and the wire are carrying the same current `I`. The current in the loop is in the counterclockwise direction if seen from above.
(q) The magnetic fields(B) at `P` due to the currents in the wires are in opposite directions.
(r) There is no magnetic field at `P`.
(s) The wires repel each other.

(4) When `d~~a` but wires are not touching the loop , it is found that the net magnetic field on the axis of the loop . In that case

A

`(mu_(0)I^(2)a^(2))/(d)`

B

`(mu_(0)I^(2)a^(2))/(2d)`

C

`sqrt(3)(mu_(0)I^(2)a^(2))/(d)`

D

`sqrt(3)(mu_(0)I^(2)a^(2))/(2d)`

Text Solution

Verified by Experts

The correct Answer is:
B
We know that torque
` vec(tau) = vec(M)xxvec(B)`
`tau = MB sin theta`
`= ( Ixxpia^(2)) xx[2xx(mu_(0)I)/( 2 pi d)] sin 30^(@)`
` = (mu_(0)I^(2)a^(2))/(2d)`
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