A and B are two infinitely long straight parallel conductors. C is another straight of length 1 m parallel to A and B . The magnitude and direction of the force experienced by C

Options

A. Towards A equal to `0.6 xx 10^(-5)` N
B. Towards B equal to `5.4 xx 10^(-5)` N
C. Towards A equal to `5.4 xx 10^(-5)` N
D. Towards B equal to `0.6 xx 10^(-5)` N

Answer

D

Explanation

Mutual force between conductors A and C,
`F_(1) = (mu_(0))/(2pi) (l_(1)l_(2)l)/(r)" "` (attractive)
`= (mu_(0))/(2pi) (2 xx 3 xx 1)/(0.05)`
`= 2.40 xx 10^(-5)`N [towards A]
Mutual force between conductors B and C (repulsive)
`= (mu_(0))/(2pi) (4 xx 3 xx 1)/(0.08) = 3 xx 10^(-4)`N [towards B]
Hence, the resultant force experienced by C
`F xx F_(2) - F_(4)`
`= (3 - 2.4) xx 10^(-5)` N
`= 0.6 xx 10^(4)`N