Biot-Savart Law

An electron makes $3\times {10}^5$ revolutions per second in a circle of radius $0.5$ angstrom. Find the magnetic field $B$ at the centre of the circle.

Consider a straight piece of length $x$ of a wire carrying a current $i$. Let $p$ be a point on the perpendicular bisector of the piece, situated at a distance $d$ from its middle point. Show that for $d\gg x$, the magnetic field at $p$ varies as $\frac{1}{d^2}$ whereas for $d\ll x$, it varies as $\frac{1}{d}$.

A current of $10 \mathrm{A}$ is established in a long wire along the positive z-axis. Find the magnetic field $\overrightarrow{\mathrm{B}}$ at the point $\left(1 \mathrm{m}, 0, 0\right)$. 

Consider three quantities $x=\frac{E}{B}, y=\sqrt{\frac{1}{{\mu }_0{\epsilon }_0}}$ and $z=\frac{l}{CR}$. Here, $l$ is the length of a wire,$C$ is the capacitance and $R$ is the resistance. All other symbols have standard meanings.

The magnetic field at the origin due to a current element $id\overrightarrow{l}$ placed at a position $\overrightarrow{r}$ is,

Two particles $X$ and $Y$ having equal charge, after being accelerated through the same potential difference enter a region of uniform magnetic field and describe circular paths of radii $R_1$ and $R_2$, respectively. The ratio of the mass of $X$ to that of $Y$ is

A particle is projected in a plane perpendicular to a uniform magnetic field. The area bounded by the path described by the particle is proportional to

A moving charge produces

A charged particle is moved along a magnetic field line. The magnetic force on the particle is

A proton beam is going from north to south and an electron beam is going from south to north. Neglecting the Earth's magnetic field, the electron beam will be deflected