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
IIT 2000, Diffcult
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(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 $PQ$.
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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