Question

Equal currents are flowing in three infinitely long wires along positive x,y and z directions.The magnetic field at a point (0,0,-a) would be (i=current in each wire):

• A. $\frac{{\mu }_{o}i}{2\pi a}(\hat{j}-\hat{i})$
• B. $\frac{{\mu }_{o}i}{2\pi a}(\hat{i}-\hat{j})$
• C. $\frac{{\mu }_{o}i}{2\pi a}(\hat{i}+\hat{j})$
• D. $\frac{{\mu }_{o}i}{2\pi a}(-\hat{i}-\hat{j})$

Answer 1

The correct option is A $\frac{{\mu }_{o}i}{2\pi a}(\hat{j}-\hat{i})$

The magnetic field due to infinite wire is $B=\frac{{\mu }_{\circ }i}{2\pi x}$, where $x$ is perpendicular distance from wire:

As point is situated on z axis, field due to wire in z direction will be zero.

Field due to wires along x and y Axis will be $B=\frac{{\mu }_{\circ }i}{2\pi a}\hat{j}$ and $B=-\frac{{\mu }_{\circ }i}{2\pi a}\hat{i}$

Total magnetic field $B=\frac{{\mu }_{\circ }i}{2\pi a}(\hat{j}-\hat{i})$