Two long parallel wires are separated by a distance of 2m. They carry a current of `1A` each in opposite direction. The magnetic induction at the midpoint of a straight line connecting these two wires is

Options

A. `(mu_(0))/(2pi)`
B. `(mu_(0))/(pi)`
C. `(2mu_(0))/(2pi)`
D. `(2mu_(0))/(pi)`

Answer

D

Explanation

The magnetic field at P due to current in P is
`B_(1) =(mu_(0))/(4pi) ((2I_(1))/(d))=(mu_(0))/(4pi) ((2xx3 )/(2)) =(3mu_(0))/(4pi)`
and the magnetic field a P due to current in the wire Q is
`B_(2) =(mu_(0))/(4pi) ((2I_(2))/(d)) =(mu_(0))/(4pi)((2xx5)/(2))=(5mu_(0))/(4pi)`
The currents in the wires are in teh opposite direction.
Hence the magnetic fields will be added.
`therefore` Resultant field `B= B_(1) + B_(2) =(3mu_(0))/(4pi)+ (5mu_(0))/(4pi)`
`therefore B = (8mu_(0))/(4pi) =(2mu_(0))/(pi)`