Two parallel conductors carry current in opposite direction as shown in figure. One conductor carries a current of 10.0 A. point C is a distance `d/2` to the right of the 10.0 A current. If the d=18 cm and l is adjusted so that the magnetic field at C is zero, the value of the current l is

Options

A. 10.0 A
B. 30.0A
C. 8.0 A
D. 18.0 A

Answer

b

Explanation

The magnetic field at C due to first conductors is `B_(1)=(mu_(0))/(2pi) l/(3d//2)` (since point C is separated by `d+d/2=(3d)/2` from 1st conductors). The direction of field is perpendicular to the plane of paper and directed outwards. The magnetic field at C due to second conductors is `B_(2)=(mu_(0))/(2pi) 10/(d//2)`(since, point C is separated by `d/2` from 2nd conductors) the direction of field is perpendicular to the plane of paper and directed inwards. since direction of `B_(1)` and `B_(2)` at point C is in opposite direction and the magnetic field at C is zero , therefore,
`B_(1)=B_(2)`
`(mu_(0))/(2pi) l/(3d//2) =(mu_(0))/(2pi) 10/(d//2)`
on solving `I=30.0 A `