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

Options

A. `(3mu_(0)Ii)/(2pi)`
B. `(mu_(0)Ii)/(2pi)log_(e)3`
C. `(mu_(0)Ii)/(2pi)log_(e)2`
D. `(2mu_(0)Ii)/(3pi)`

Answer

B

Explanation

Consider an element of length `dx` on `AB` at a distance `x` from `XY`.

Force on this element, `dF=(mu_(0)I)/(2pix)idx`
Total force on `dF=(mu_(0)I)/(2pix)idx`
`(mu_(0)li)/(2pi)int_(l//2)^(3l//2)(1)/(x)dx=(mu_(0)li)/(2pi)log_(e)3`