Question

An infinitely long conductor $PQR$ is bent to form a right angle as shown. A current $I$ flows through $PQR$. The magnetic field due to this current at the point $M$ is $H_1$. Now, another infinitely long straight conductor $QS$ is connected at $Q$, so that the current is $1/2$ in $QR$ as well as in $QS$. The current in $PQ$ remaining unchanged. The magnetic field at $M$ is now $H_2$. The ratio $H_1/H_2$ is given by

• A. $\frac{1}{2}$
• B. 1
• C. $\frac{2}{3}$
• D. 2

Answer 1

Answer: (C)

Magnetic field at any point lying on the current-carrying straight conductor is zero.
Here, $H_1=$ magnetic field at $M$ due to current in $PQ$.
$H_2=$ magnetic field at $M$ due to $QR+$ magnetic field at $M$ due to $QS+$ magnetic field at $M$ due to $PQ$.
$=0+\frac{H_1}{2}+H_1=\frac{3}{2}{H}_1$
$\Rightarrow \frac{H_1}{H_2}=\frac{2}{3}$