Biot-Savart’s Law

A particle carrying a charge equal to $100$ times the charge on an electron is rotating one rotation per second in a circular path of radius $0.8 \mathrm{m}$. The value of the magnetic field produced at the centre will be (${\mu }_0=$ permeability for vacuum)

Biot-Savart law indicates that the moving electrons (velocity $v$) produce a magnetic field $B$ such that:

A small current element of length $\mathrm{d}l$ and carrying current $i$ is placed at $(1,1,0)$ and is carrying current in $+z$ direction. If the magnetic field at origin be ${\overrightarrow{B}}_1$ and at point $(2,2,0)$ be ${\overrightarrow{B}}_2$ then 

Calculate the magnetic field at the centre of a coil in the form of a square of side $2a$ carrying a current $I$.

A current $I$ flows in the anticlockwise direction through a square loop of side $a$ lying in the $xy$ plane with its centre at the origin. The magnetic induction at the centre of the square loop is:

The region surrounding a stationary electric dipole has,

If the current flowing in a circular loop is in clockwise direction, then the magnetic induction will be,

According to right-hand thumb rule, if current is directed in upward direction then the direction of magnetic induction is,

The direction of magnetic field produced around a long straight conductor is given by,

In vector form, the magnetic induction $dB$ at a point of distance $r$ from centre of element of length $dl$ is given as,

The dimension and $\mathrm{SI}$ unit of permeability of free space $\left({\mu }_0\right)$ are,

The magnetic field produced around a straight line wire when current flows through it is,

The value of magnetic induction will be minimum at a point due to a small current carrying conductor when angle between element and line joining point and centre of element is,

The magnitude of magnetic induction at a point due to a small current carrying conductor is,

The phenomenon in which magnetic field is produced in the space near a conductor carrying current is called,

Choose the correct option regarding the magnetic field $\overrightarrow{B}$ produced by an electron moving with velocity $\overrightarrow{\mathit{v}}$.

A  current element of length $dl$ and carrying current $I$ in $+z$ direction is placed at $(1,1,0)$. If the magnetic field at origin is $\overrightarrow{B_1}$ and at point $(2,2,0)$ is $\overrightarrow{B_2}$, then, 

An infinitely long hollow conducting cylinder with inner radius $\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $\left|\overrightarrow{B}\right|$ as a function of the radial distance $r$ from the axis, is best represented by:

One of the two identical conducting wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the centre of the loop $\left(B_L\right)$ to that at the centre of the coil $\left(B_C\right),$ i.e. $\frac{B_L}{B_C}$ will be