Question

Two long straight parallel wires in which there are currents of 2.0A and 3.0A respectively in the same direction are 0.1m apart. Calculate the magnetic field at a point mid-way between them

Answer 1

Magnetic field at a point mid-way between the wires due to the Ist wire:
$B_1=\frac{{\mu }_{0}1}{2\pi r}=\frac{4\pi \times {10}^{-7}\times 2}{2\pi \times 0.05}=8.0\times {10}^{-6}Wb/m^2$

Magnetic field at the point mid-way between the wires, due to the second wire,
$B_2=\frac{{\mu }_{0}I}{2\pi r}=\frac{4\pi \times {10}^{-7}\times 3}{2\pi \times 0.05}$$=12\times {10}^{-6}Wb/m^2$ (outwards the plane of the paper)

Hence, the resulting field at the point:
$B_2-B_1=12\times {10}^{-6}-8\times {10}^{-6}$$=4\times {10}^{-6}Wb/m^2$ (outwards the plane of the paper)