Exercise - 1

Find the magnetic field at the centre of a square of side $a$ carrying current $1 \mathrm{A}$.

A tightly-wound, long solenoid is kept with its axis parallel to a large metal sheet carrying a surface current. The surface current through the width $dl$ of the sheet is $Kdl$ and the number of turns per unit length of the solenoid is $n$. The magnetic field near the centre of the solenoid is found to be zero,

$\left(\mathrm{a}\right)$ Find the current in the solenoid. $\left(\mathrm{b}\right)$ If the solenoid is rotated to make its axis perpendicular to the metal sheet, what would be the magnitude of the magnetic field near its centre?

A tightly-wound, long solenoid has $n$ turns per unit length, a radius $r$ and carries a current $i$. A particle having charge $q$ and mass $m$ is projected from a point on the axis in a direction perpendicular to the axis. What can be the maximum speed for which the particle does not strike the solenoid?

A particle $\left(\mathrm{a}\right)$ mass $m$ and charge $q$ is released at rest at the origin in a region in which there are electric and magnetic fields given by, $\overrightarrow{B}=-B_0\hat{\mathrm{j}}$ and $\overrightarrow{E}=-E_0\hat{\mathrm{k}}$. Find the speed of the particle as a function of its $Z-$ coordinate.

A circular coil of $100$ turns and having an effective radius of $0.05 \mathrm{m}$ carries a current of $0.1 \mathrm{A}$. How much work is required to turn it in an external magnetic field of $1.5 \mathrm{Wb} {\mathrm{m}}^{-2}$ through $180°$ about an axis perpendicular to the magnetic field. The plane of the coil is initially perpendicular to the magnetic field

A current $I$ flows along the length of an infinitely long, straight and thin-walled pipe. Then 

Two particles $X$ and $Y$ having equal charges, after being accelerated through the same potential difference enter a region of uniform magnetic field and describes circular paths of radii $r_1$ and $r_2$ respectively. The ratio of the mass of $X$ and $Y$ is 

A conducting circular loop of radius $\mathrm{r}$ carries a constant current i. It is placed in a uniform magnetic field $\mathrm{B}$ such that $\mathrm{B}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is