Two very thin metallic wires placed along $X$ and $Y$-axis carry equal currents as shown here. $AB$ and $CD$ are lines at $45^\circ $ with the axes with origin of axes at $O$. The magnetic field will be zero on the line

Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\,m$ and $0.2\,m$ from the centre are in the ratio $8 : 1$. The radius of the coil is.....$m$

Two circular coils $X$ and $Y$, having equal number of turns, carry equal currents in the same sense and subtend same solid angle at point $O$. If the smaller coil, $X$ is midway between $O$ and $Y$, then if we represent the magnetic induction due to bigger coil $Y$ at $O$ as $BY$ and that due to smaller coil $X$ at $O$ as $BX$ , then

Math List $I$ with List $II$

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An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to

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