Question

Two parallel wires of equal lengths are separated by a distance of 3m from each other. The currents flowing through first and second wire is 3A and 4.5A respectively in opposite directions. The resultant magnetic field at the mid-point of both wire is (µ₀ = permeability of free space).

Options

• `(7mu_0)/(2pi)`

• `mu_0/(2pi)`

• `(3mu_0)/(2pi)`

• `(5mu_0)/(2pi)`

Answer 1

`(5mu_0)/(2pi)`

Explanation:

The currents are in opposite direction and hence their fields are in same direction at the midpoint which is at a distance of 1.5 m from each wire. 

`"B"_1 = mu_0/(2pi) "I"_1/"r" = mu_"o"/(2pi) * 3/1.5 = (2mu_"o")/(2pi)` 

`"B"_2 = mu_"o"/(2pi) "I"_2/"r" = mu_0/(2pi) * 4.5/1.5 = (3mu_"o")/(2pi)`

`therefore "B" = "B"_1 + "B"_2 = (5mu_"o")/(2pi)`