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 I/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 $\frac{H_1}{H_2}$ is given by

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

Answer 1

The correct option is C $\frac{2}{3}$

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
$=0+\frac{H_1}{2}+H_1=\frac{3}{2}{H}_1\Rightarrow \frac{H_1}{H_2}=\frac{2}{3}$