Question

Two long parallel wires situated at a distance $2a$ are carrying equal current ‘$i$’ in opposite direction as shown in figure. The value of magnetic field at a point $P$ situated at equal distance $\left(r\right)$ from both the wires is

• A. $\frac{{\mu }_{0}ia}{\pi r}$
• B. $\frac{{\mu }_{0}i{a}^2}{\pi r}$
• C. $\frac{{\mu }_{0}i{a}^2}{\pi r^2}$
• D. $\frac{{\mu }_{0}ia}{\pi r^2}$

Answer 1

The correct option is D $\frac{{\mu }_{0}ia}{\pi r^2}$


Magnetic field due to infinite long wire is $B=\frac{{\mu }_{0}i}{2\pi r}$

From the rightangled triangle shown, $\sin \theta =\frac{a}{r}$

$B_{net}=2B\sin \theta =\frac{2{\mu }_{0}ia}{2\pi r.r}=\frac{{\mu }_{0}ia}{\pi r^2}$