Question

Two long straight wires are set parallel to each other Each carries a current $i$ in the opposite direction and the separation between them is 2R. The intensity of the magnetic field midway between them is

• A. zero
• B. $ \frac{{{\mu }_{0}}i}{4\pi R} $
• C. $ \frac{{{\mu }_{0}}i}{2\pi R} $
• D. $ \frac{{{\mu }_{0}}i}{\pi R} $

Answer 1

Answer: (B)

Magnetic field at mid point due to wire AB
$ {{B}_{1}}=\frac{{{\mu }_{0}}i}{2\pi R} $
Magnetic field at midpoint due to wire CD
$ {{B}_{2}}=\frac{{{\mu }_{0}}i}{2\pi R} $
Resultant of Magnetic field
$ B={{B}_{1}}+{{B}_{2}} $
$ =\frac{{{\mu }_{0}}i}{2\pi R}+\frac{{{\mu }_{0}}i}{2\pi R} $
$ B=\frac{{{\mu }_{0}}i}{\pi R} $