Two long parallel wires `P` and `Q` are both perpendicular to the plane of the paper with distance `5m` between them. If `P` and `Q` carry current of `2.5` amp and `5` amp respectively in the same direction, then the magnetic field at a point half way between the wires is

Options

A. `(sqrt(3) mu_(0))/(2pi)`
B. `(mu_(0))/(pi)`
C. `(3 mu_(0))/(2pi)`
D. `(mu_(0))/(2pi)`

Answer

D

Explanation

In the following figure, magnetic field at mid point `M` is given by,

`B_(net) = B_(Q) - B_(P)`
`= (mu_(0))/(4pi). (2)/(r) (i_(Q) - i_(p))`
`= (mu_(0))/(4pi) xx (2)/(2.5) (5 - 2.5) = (mu_(0))/(2pi)`