$A$ proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow{E}$ and $\overrightarrow{B}$ represent the electric and magnetic fields respectively,then this region of space may have

$A$ long,straight wire is turned into a loop of radius $10\,cm$ (see figure). If a current of $8\,A$ is passed through the loop,then the value of the magnetic field and its direction at the centre $C$ of the loop shall be close to

$A$ long thin-walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to the quarter portion of the pipe shown is:

The dimensional formula of $\frac{1}{2} \mu_0 H^2$ (where $\mu_0$ is the permeability of free space and $H$ is the magnetic field intensity) is:

Two parallel long wires carry currents $i_1$ and $i_2$ with $i_1 > i_2$. When the currents are in the same direction,the magnetic field midway between the wires is $10 \, \mu T$. When the direction of $i_2$ is reversed,it becomes $40 \, \mu T$. The ratio $i_1/i_2$ is

Two charged particles $A$ and $B$,each of charge $+e$ and masses $12 \, amu$ and $13 \, amu$ respectively,follow a circular trajectory in chamber $X$ after passing through a velocity selector as shown in the figure. Both particles enter the velocity selector with a speed of $1.5 \times 10^6 \, ms^{-1}$. $A$ uniform magnetic field of strength $1.0 \, T$ is maintained within the chamber $X$ and in the velocity selector,directed into the plane ($-z$ direction).