A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5m apart, in the negative Z-direction. A point P is at a perpendicular distance 3m from the first wire and 4m from the second. What will be magnitude of the magnetic field `vec(B)` at P?

Options

A. `(5)/(12) (mu_(0I)`
B. `(7)/(24) (mu_(0)I)`
C. `(5)/(24) (mu_(0)I)`
D. `(25)/(288) (mu_(0)I)`

Explanation

Here is this case from the given data, magnetic field due to first wire, `B_(1)= (mu_(0)I)/(2pi xx 3)` and magnetic field due to second wire, `B_(2)= (mu_(0)I)/(2pi xx 4)`
`:.` Net magnetic field at point P, `B= sqrt(B_(1)^(2)+ B_(2)^(2))= (mu_(0)I)/(2pi) sqrt((1)/(9) + (1)/(16))= (mu_(0)I)/(2pi) xx sqrt((25)/(9 xx 16))= (mu_(0)I)/(2pi) xx (5)/(12)= (5mu_(0)I)/(24pi)`
None of the given options is correct