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An infinitely long current carrying wire...

An infinitely long current carrying wire and a small current carrying wire and a small current carrying loop are in the plane of thye paper as shown. The ardius of the loop is a and distance of its centre from the wire is d (dgtgta). If the loop applies a force F on the wire then :

A

F = 0

B

`F prop (a/d)^2`

C

`F prop (a^2/d^3)`

D

`F prop (a/d)`

Text Solution

Verified by Experts

The correct Answer is:
B

Force one pole
`F=mxx(mu_0I)/(2pisqrt(d^2+x^2))`
Total force `=2F sin theta`
`=2 xx(mu_0Im)/(2pisqrt(d^2+a^2))xxx/(sqrt(d^2+a^2))implies(mu_0Imx)/(pi(d^2+a^2))`
`m xx 2 = M = I xx pia^2` ( magnetic moment)
Total force `=(mu_0Ia^2)/(2(d^2+a^2))implies (mu_0Ia^2)/(2d^2)" "` (As ` d gt gt a`)
`implies F_(tau) prop (a/d)^2`
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