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 due to first conductor is `B_(1)=(mu_(0))/(2pi)(i)/((3d)/(2))` (Since Point C is separated by `d+(d)/(2)=(3d)/(2)` from `1^(st)` conductor)
The direction of field is perpendicular to the plane of paper and directed outward. The magnetic field at due to second conductor is `B_(2)=(mu_(0))/(2pi)(10)/((d)/(2))` (Since, Point C is separated by `(d)/(2)` from `2^(nd)` conductor)
The direction of field is perpendicular to the plane of paper and directed inward.
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))/(2)(i)/((3d)/(2))=(mu_(0))/(2pi)(10)/((d)/(2))`
On solving i=30.0A