Question

Figure shows an arrangement in which four long parallel wires carrying equal current are placed at the corners of a square. The direction of current is as shown, either into the plane or outwards. The magnetic field at the centre of the square is

• A. $\frac{{\mu }_{0}I}{2\pi r}\sqrt{2}$
• B. $\frac{{\mu }_{0}I}{\pi r}\sqrt{2}$
• C. $\frac{4{\mu }_{0}I}{2\pi r}$
• D. Zero

Answer 1

The correct option is D Zero

The direction of magnetic field at point $O$ due to all four current carrying wire can be find by using right- hand thumb rule and this is shown in below diagram.


Here, $O$ is equidistant from all four corners of the square and all four corner wires carry equal current $i$.

$\therefore \left|\overrightarrow{B}\right|$ due to any of $4$ corner wires at centre $O$ will be same

$\therefore \left|\overrightarrow{B_M}\right|=\left|\overrightarrow{B_N}\right|=\left|\overrightarrow{B_R}\right|=\left|\overrightarrow{B_S}\right|=\frac{{\mu }_{0}i}{2\pi r}$

From the above diagram, we can observe that $B_N$ and $B_S$ are opposite in direction and equal in magnitude, so they get cancelled. Similarly, $B_M$ and $B_R$ gets canceled.

So, net magnetic field at centre of the square will ve zero.

Therefore, option $\left(d\right)$ is the correct answer.