Question

Two long parallel wires carry equal current $i$ flowing in the same direction are at a distance $2d$ apart. The magnetic field $B$ at a point lying on the perpendicular line joining the wires and at a distance $x$ from the midpoint is -

• A. $\frac{{\mu }_{0}id}{\pi \left(d^2+x^2\right)}$
• B. $\frac{{\mu }_{0}ix}{\pi \left(d^2-x^2\right)}$
• C. $\frac{{\mu }_{0}ix}{\left(d^2+x^2\right)}$
• D. $\frac{{\mu }_{0}id}{\left(d^2+x^2\right)}$

Answer 1

Answer: (B)

The magnetic field due to two wires at $P$
$B_1=\frac{{\mu }_{0}i}{2\pi (d+x)};B_2=\frac{{\mu }_{0}i}{2\pi (d-x)}$
Both the magnetic fields act in opposite direction.
$\therefore B=B_2-B_1$
$=\frac{{\mu }_{0}i}{2\pi }\left[\frac{1}{d-x}-\frac{1}{ds+x}\right]$
$=\frac{{\mu }_{0}i}{2\pi }\left[\frac{d+x-d+x}{d^2-x^2}\right]$
$=\frac{{\mu }_{0}ix}{\pi \left(d^2-x^2\right)}.$