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A conductor AB of length l carrying curr...

A conductor `AB` of length `l` carrying current `i` is placed perpendicular to a long straight conductor carrying a current `I` as shown. Force on `AB` will be

A

`(3mu_(0)Ii)/(2 pi)`

B

`(mu_(0)Ii)/(2 pi)log_(e)3`

C

`(mu_(0)Ii)/(2 pi)log_(e)2`

D

`(2mu_(0)Ii)/(3 pi)`

Text Solution

Verified by Experts

The correct Answer is:
B
Consider an element of length dx on AB at a distance x from XY.
Force on this element, `dF=(mu_(0)I)/(2 pi x)idx`
Total force on `dF=(mu_(0)I)/(2 pi x) idx`
`=(mu_(0)I)/(2 pi) int_(l//2)^(3l//2) 1/x dx =(mu_(0)Ii)/(2 pi)log_(e)3`.
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