Question

Each of two long parallel wires carries a constant current $i$ along the same direction.The wires are separated by a distance $2l$.The magnitude of resultant magnetic induction in the symmetric plane of this system located between the wires at a distance $R$ from each wire will be:

• A. $\frac{{\mu }_{0}i}{\pi R}$
• B. $0$
• C. $\frac{{\mu }_{0}i}{\pi \sqrt{R^2-l^2}}$
• D. $\frac{{\mu }_{0}i}{\pi R}\sqrt{1-\frac{l^2}{R^2}}$

Answer 1

The correct option is B $0$

Let us consider a point P on the symmetric plane which is at distance R from the wires.
Using Amper's law,
$\overrightarrow{B}=\frac{{\mu }_{0}i}{2\pi R}$
Since the currents are equal and in the same direction, the magnetic field at P due to one will be equal and opposite to that due to other wire.
Hence, net magnetic field at P is zero.