Question

An infinitely long conductor PQR is bent to form a right angle as shown in figure. 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 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 $H_1/H_2$ is given by

• A. 1/2
• B. 1
• C. 2/3
• D. 2

Answer 1

Answer: (C)

$H_1$ = Magnetic field at M due to PQ + Magnetic field at M due to QR
But magnetic field at M due to QR = 0
$\therefore$ Magnetic field at M due to PQ (or due to current 1 in PQ)$=H_1$
Now $H_2$ = Magnetic field at M due to PQ (current I)
+ magnetic field at M due to QS (current 1/2)
+ magnetic field at M due to QR
$=H_1+\frac{H_1}{2}+0=\frac{3}{2}{H}_1$
$\frac{H_1}{H_2}=\frac{2}{3}$
NOTE Magnetic field at any point lying on the current carrying straight conductor is zero.