Question

A steady current I is flowing in the x- direction through each of two infinitely long wires at $y=\pm \frac{L}{2}$ as shown in the figure. The permeability of the medium is ${\mu }_0$. The $\overrightarrow{B}$ field at (0, L, 0 ) is

• A. $-\frac{4{\mu }_{0}I}{3\pi L}\hat{z}$
• B. $+\frac{4{\mu }_{0}I}{3\pi L}$
• C. 0
• D. $-\frac{3{\mu }_{0}I}{4\pi L}\hat{z}$

Answer 1

The correct option is A $-\frac{4{\mu }_{0}I}{3\pi L}\hat{z}$

Ans : (a)

$\overrightarrow{B}=\frac{{\mu }_{0}I}{2\pi \left(\frac{L}{2}\right)}(-\hat{z})+\frac{{\mu }_{0}I}{2\pi \left(\frac{3L}{2}\right)}(-\hat{z}$)
= $\frac{{\mu }_{0}I(-\hat{z})}{2\pi L}(2+\frac{2}{3})=-\frac{4}{3}\frac{{\mu }_{0}I}{\pi L}\hat{z}$