A constant direct current of uniform density $\hat{j}$ is flowing in an infinitely long cylindrical conductor. The conductor contains an infinitely long cylindrical cavity whose axis is parallel to that of the conductor and is at a distance $\stackrel{\rightharpoonup }{\mathcal{l}}$ from it. What will be the magnetic induction $\stackrel{\rightharpoonup }{B}$ at a point inside the cavity at a distance $\stackrel{\rightharpoonup }{r}$ from the centre of cavity?

The given fig. shows a coil bent with $\mathrm{AB} = \mathrm{BC} = \mathrm{CD} = \mathrm{DE} = \mathrm{EF} = \mathrm{FG} = \mathrm{GH} = \mathrm{HA} = 1 \mathrm{m}$ and carrying current $1 \mathrm{A}$. There exists in space a vertical uniform magnetic field of $2 \mathrm{T}$ in the y-direction. The torque on the loop is.

In a region magnetic field along $x-$axis changes with time according to the given graph.

If time period, pitch and radius of projected path are $T_0, P_0$ and $R_0$, respectively then which of the following is incorrect if the positively charged particle is projected at an angle ${\mathrm{\theta }}_0$ with the positive $x-$axis in $x-y$ plane from origin:

A horizontal metallic rod of mass $m$ and length $\mathcal{l}$ is supported by two vertical identical springs of spring constant $K$ each and natural length ${\mathcal{l}}_0$. A current $i$ is flowing in the rod in the direction shown. If the rod is in equilibrium then the length of each spring in this state is

A non-planer loop of conducting wire carrying a current $I$ is placed as shown in the figure. Each of the straight sections of the loop is of length $2a$. The magnetic field due to this loop at the point $\mathrm{P}(\mathrm{a}, 0, \mathrm{a})$ points in the direction.