Two thin long parallel wires seperated by a distance 'b' are carrying a current ' I' amp each . The magnitude of the force3 per unit length exerted by one wire on the other is

Options

A. `(mu_(0)i^(2))/(b^(2))`
B. `(mu_(0)i^(2))/(2pib)`
C. `(mu_(0)i)/(2pib)`
D. `(mu_(0)i)/(2pib^(2))`

Answer

B

Explanation

when two infinitely long parallel long parallel conductors carrying currents `i_(1)` and `i_(2)` are placed a distane r apart then force on the unit length of a coinductor due to the other conductor is given by
`F=(mu_(0))/(4pi)(2 i_(1)i_(2))/(r )`
here `i_(1)=i_(2)=i` and r=b
`therefore F=(mu_(0)i^(2))/(rpib)`