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A conductor AB of length L carrying a cu...

A conductor AB of length L carrying a current `I_(2)`, IS placed perpendicular to a long straight conductor XY carrying current `I_(2)`, as shown in figure. The force on AB in magnitude is

A

`(3mu_(0)I_(1)I_(2))/(2pi)`

B

`(mu_(0)I_(1)I_(2))/(2pi) In 2`

C

`(2mu_(0)I_(1)I_(2))/(3pi) `

D

`(mu_(0)I_(1)I_(2))/(2pi) In 2`

Text Solution

Verified by Experts

The correct Answer is:
C
Consider an element of length dx on AB at a distance x from XY. Force on the element is

`dF=(mu_(0))/(4pi)(2l_(1))/(x)xxI_(2)xxdx=(mu_(0)I_(1)I_(2))/(2pi)(dx)/(x)`
Total forece on AB is
`F = mu_0/(2pi) I_1I_2int_(L//2)^(3L//2) (dx)/(x) = (mu_0 I_1I_2)/(2pi) ln 3`
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