Question

Two long parallel wires are at a distance $2d$ apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Answer 2

The magnetic field in between because of each will be in opposite direction $B_{in\, between} = \frac{\mu_{0}i}{2\pi x}\hat{j} - \frac{\mu _{0}i}{2\pi \left(2d-x\right)}\left( -\hat{j}\right)$ $\frac{\mu _{0}i}{2\pi }\left[\frac{1}{x}- \frac{1}{2d-x}\right]\left( \hat{j}\right)$ $\begin{matrix}at&x = d,&B_{in\, between} = 0\\\ for&x < d,&B_{in\, between} = \left( \hat{j}\right)\\\ for&x > d,&B_{in\, between} =\left( -\hat{j}\right) \end{matrix}$ towards x net magnetic field will add up and direction will be $\left(- \hat{j}\right)$ towards x' net magnetic field will add up and direction will be $\left( \hat{j}\right)$