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
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$\mathrm{H}_{1}=$ 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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