Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

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 $QS$,while the current in $PQ$ remains unchanged. The magnetic field at $M$ is now $H_2$. The ratio $H_1/H_2$ is given by

The magnetic field at the origin due to the current $I$ flowing in the wire as shown in the figure is:

The unit of permeability of vacuum $(\mu_{0})$ is . . . . . . .

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper,as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

The unit vectors $\hat{i}, \hat{j},$ and $\hat{k}$ are as shown below. What will be the magnetic field at $O$ in the following figure?