A long straight wire along the $z$-axis carries a current $I$ in the negative $z$-direction. The magnetic vector field $\overrightarrow{\mathit{B}}$ at a point having coordinates $(x, y)$ in the $z=0$ plane is 

A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius $R_1$ & the outer conductor is hollow of inner radius $R_2$ and outer radius $R_3$. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as

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.