The resultant force on the current loop PORS due to a long current carrying conductor, as shown will be

Options

A. `1.8xx10^(-4)N`
B. `5xx10^(-4)`
C. `10^(-4)`
D. `3.6xx10^(-4)`

Answer

B

Explanation

Refer figure The effective force is only on the arm SP and QR.The force `(F_(1))` on the arm SP is attractive and force `(F_(2))` on arm QR is repulsive. There fore effective force is
`F=F_(1)-F_(2)=(mu_(0))/(2pi)(2I_(1)I_(2)l)/(r)-(mu_(0))/(4pi)(2I_(1)I_(2)l)/((r+d))`
`=(mu_(0))/(4pi)2I_(1)I_(2)l[(1)/(r)-(1)/((r+d))]`
Here l=15cm, r=2cm,d=10cm,`I_(1)=I_(2)`=20A
`.F=10^(-7)xx2xx20xx20xx0.15[(1)/(0.02)(1)/(0.12)]=5xx10^(-4)N`