Q. Two long parallel wires carry equal current $i$ flowing in the same direction area at a distance $2d$ apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and a distance $x$ from the midpoint is
A) $EQ\ \frac{\mu_{0}id}{\pi(d^{2} + x^{2})}$
B) $\frac{\mu_{0}ix}{\pi(d^{2} - x^{2})}$
C) $\frac{\mu_{0}ix}{(d^{2} + x^{2})}$
D) $\frac{\mu_{0}id}{(d^{2} - x^{2})}$
Explanation
(b) The magnetic field due to first wire
$B_{1} = \ \frac{\mu_{0}i}{2\pi(d + x)}$
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$B_{2} = \ \frac{\mu_{0}i}{2\pi(d - x)}$
Both the magnetic field act in opposite direction.
$\therefore\ B = B_{2} - B_{1} = \frac{\mu_{0}}{2\pi}\left\lbrack \frac{1}{d - x} - \frac{1}{d + x} \right\rbrack$
=$\ \frac{\mu_{0}i}{2\pi}\ \left\lbrack \frac{d + x - d + x}{d^{2} - x^{2}} \right\rbrack = \frac{\mu_{0}ix}{\pi(d^{2} - x^{2})}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.