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 distances from both the wires will be:

• 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 $\frac{{\mu }_{0}ia}{\pi r^2}$

The fields due to both $\left(1\right)$ and $\left(2\right)$ have magnitude $B_1=B_2=\frac{{\mu }_{o}i}{2\pi r}$ and in the directions as shown in the figure.
Magnetic field at $P$ is $B_P=B_1\sin \theta +B_2\sin \theta$
$B_P=2B_1\sin \theta$
$B_P=2\times \frac{{\mu }_{0}i}{2\pi r}\times \frac{a}{r}$ $(\because \sin \theta =\frac{a}{r})$
$B_P=\frac{{\mu }_{0}ia}{\pi r^2}$