Two parallel wires of length 9 m each, are separated by a distance of 0.15 m. If they carry equal current in the same direction and exert a total force of `30xx10^(-7)N` on each other, the value of the current must be

Options

A. 1.5 A
B. 2.25 A
C. 0.5 A
D. 0.25 A

Answer

C

Explanation

Force between two wires caryying current, `F=(mu_(0))/(2pi)(i_(1)i_(2))/(r)I`
Given `F=30xx10^(-7)N, r=0.15m, i_(1)=i_(2)=i_(1), I_(1)=I_(2)=I=9m`
`30xx10^(-7)=2xx10^(-7)(i.i)/(0.15)xx9`
`implies i^(2)=(30xx10^(-7)xx0.15)/(2xx10^(-7)xx9)=1/4`
`therefore i=1/2=0.5 A`