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 along the line $XX'$is given by

Question

Dr. Abubacker · Accepted Answer

(a) The magnetic field in between because of each will be in opposite direction
$B_{in\ between} = \frac{\mu_{0}i}{2\pi x}\ \widehat{\mathbf{J}} - \frac{\mu_{0}i}{2\pi\ (2d - x)}\ ( - \widehat{\mathbf{j}})$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = \frac{\mu_{0}i}{2\pi}\left\lbrack \frac{1}{x} - \frac{1}{2d - x} \right\rbrack\ (\widehat{\mathbf{j}})$
At $x = d,\ B_{in\ between} = 0$
For $x < d,\ B_{in\ between\ } = (\widehat{\mathbf{j}})$
For $x > d,\ B_{in\ between} = ( - \widehat{\mathbf{j}})$
Towards $x,$ net magnetic field will add up and direction will be $\left( - \widehat{\mathbf{j}} \right)\mathbf{.}$
Towards $x^{'},$ net magnetic field will add up and direction will be $\left( - \widehat{\mathbf{j}} \right)\mathbf{.}$

Q. 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 along the line $XX'$is given by

Explanation

Reviewed by Dr. Abubacker

Want more practice?