Academic Experts Solutions for Chapter: Moving Charges and Magnetism, Exercise 1: Magnetic Field

A long straight wire, carrying current $I$, is bent at its midpoint to form an angle of $45°$. Find the magnetic field at a point $P$, which is at a distance $R$ from the point of bending.

The magnitude of magnetic field at $O$ (Centre of the circular part) of the current carrying coil as shown is 

$A$ and $B$ are two concentric circular conductors of centre $O$ and carrying current $i_1$ and $i_2$, respectively as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the flux densities at $O$ due to $A$ and $B$ is $1:3$, then the value of $\frac{i_1}{i_2}$ will be

Two concentric coils, each of radius equal to $2\pi \mathrm{cm}$, are placed at right angles to each other. Currents $3 \mathrm{A}$ and $4 \mathrm{A}$ are flowing in each coil, respectively. The magnetic induction (in $\mathrm{Wb} {\mathrm{m}}^{-2}$) at the centre of the coils will be  $\left({\mu }_0=4\pi \times {10}^{-7} \mathrm{Wb} \mathrm{A} {\mathrm{m}}^{-1}\right)$,

A linear small part of a circuit $PQ$ is situated on $x$ axis from $x=-\frac{a}{2}$ to $x=+\frac{a}{2}$ and a current $I$ is flowing through it. The magnetic field produced due to part $PQ$ at point $x=+a$ will be

Magnetic field at point $P$ due to given current distribution is 

The magnetic field due to a straight conductor of uniform cross section of radius $a$ and carrying a steady current is represented by

The current density $\overrightarrow{J}$ inside a long solid cylindrical wire of radius $a=12 \mathrm{mm}$ is in the direction of the central axis and its magnitude varies linearly with radial distance $r$ from the axis according to $J=\frac{J_{0}r}{a}$ where, $J_0=\frac{{10}^5}{4\mathrm{\pi }} \mathrm{A} {\mathrm{m}}^{-2}$. Find the magnitude of the magnetic field at $r=\frac{a}{2}$in $\mathrm{\mu T}$.