A segment `AB` of wire carrying current `I_1` is placed perpendicular to a long straight wire carrying current `I_2` as shown in figure. The magnitude of force experienced by the straight wire `AB` is

Options

A. `(mu_0I_1I_2)/(2pi)ln 3`
B. `(mu_0I_1I_2)/(2pi) ln 2`
C. `(2mu_0I_1I_2)/(2pi)`
D. `(mu_0I_1I_2)/(2pi)`

Answer

B

Explanation

At a distance X from current `I_2`
`B=mu_0/(2pi)I_2/X`
Magnetic force of small element `dX` of wire `AB`
`dF=I_2(dX)Bsin90^@`
`:. F=int_(x=a)^(x=2a) dF`