An infinitely long conductor PQR is bent to from a right angle as… - Vidyadip

MCQ

An infinitely long conductor $PQR$ is bent to from 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 in $PQ$ remaining unchanged. The magnetic field at $M$ is now $H_2$ . The ratio $H_1/H_2$ is given by

A
$0.5$
B
$1$
✓
$0.67$
D
$2$

✓

Answer

Correct option: C.

$0.67$

c
$\mathrm{H}_{1}=$ Magnetic field at $\mathrm{M}$ due to $\mathrm{PQ}+$ Magnetic field at $M$ due to $QR$

But magnetic field at $\mathrm{M}$ due to $\mathrm{QR}=0$

Now $\quad \mathrm{H}_{2}=$ Magnetic field at $\mathrm{M}$ due to $\mathrm{PQ}$ (cument $\mathrm{I}$ )

$+$ Magnetic field at $M$ due to $QS$ (current $1/2$)

$+$ Magnetic field at $M$ due to $QR$

$=\mathrm{H}_{1}+\frac{\mathrm{H}_{1}}{2}+0=\frac{3}{2} \mathrm{H}_{1}$

$\therefore \quad \frac{\mathrm{H}_{1}}{\mathrm{H}_{2}}=\frac{2}{3}$

Magnetic field at any point lying on the current carrying straight conductor is zero.

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