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

MCQ

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 ${H_1}/{H_2}$ is given by

A
$0.5$
B
$1$
✓
$0.67$
D
$2$

✓

Answer

Correct option: C.

$0.67$

c
(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}$

$==>$$\frac{{{H_1}}}{{{H_2}}} = \frac{2}{3}$

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