Exercise

A circular current-carrying coil has a radius $R$. The distance from the centre of the coil on the axis of the coil, where the magnetic induction is $\frac{1}{8}$th of its value at the centre of the coil is

An electron having mass $\left(9.1\times {10}^{-31} \mathrm{kg}\right)$ and charge $\left(1.6\times {10}^{-19} \mathrm{C}\right)$ moves in a circular path of radius $0.5 \mathrm{m}$ with a velocity ${10}^6 \mathrm{m} {\mathrm{s}}^{-1}$ in a magnetic field. Strength of magnetic field is

Two long straight wires are set parallel to each other. Each carries a current $i$ in the same direction and separation between them is $2 r$. Intensity of magnetic field midway between them is

A moving coil galvanometer has a coil of effective area $\mathrm{A}$ and number of turns $\mathrm{N}$. The magnetic field $\mathrm{B}$ is radial. If a current $I$ is passed through the coil, the torque acting on the coil is

The magnetic field near a current carrying conductor is given by 

A solenoid $1.5 \mathrm{m}$ long and $0.4 \mathrm{cm}$ in diameter possesses $10$ turns per $\mathrm{cm}$ length. A current of $5 \mathrm{A}$ flows through it. The magnetic field at the axis inside the solenoid is

A circular coil of $20$ turns and radius $10 \mathrm{cm}$ is placed in an uniform magnetic field of $0.1 \mathrm{T}$ normal to the plane of the coil. The coil carries a current of $5 \mathrm{A}$. The coil is made up of copper wire of cross-sectional are ${10}^{-5} {\mathrm{m}}^2$ and the number of free electrons per unit volume of copper is ${10}^{29}$. The average force experienced by an electron in the coil due to magnetic field is 

The radius of the path of a charged particle orbiting in a uniform magnetic field is