Embibe Experts Solutions for Exercise 3: EXERCISE

Find $\oint \overrightarrow{B}·\overrightarrow{dl}$ over following loops (direction in which integration has to be performed is indicated by arrows)

Two infinite sheets of current are carrying current $\lambda$ per unit length as shown in figure. Find magnetic field at points $A, B$ and $C.$

A solid thin wire is located inside two $co$-axial long cylindrical shells, each carrying current $i$ as shown in figure. Assuming wires to be infinitely long, find magnetic field at a point which is at a distance $x$ from the axis. Assume that $a<x<b.$

A solid current carrying conductor of radius $R$ is having current per unit area $\left(J\right)$ as $J=\frac{\alpha r}{R}$ where $\alpha$ is a constant and $r$ is distance from axis. Find magnetic field at distance $x$ from axis of wire. Assume $x>R.$

A solid current carrying conductor of radius $R$ is having current per unit area $\left(J\right)$ as $J=\frac{\alpha r}{R}$ where $\alpha$ is a constant and $r$ is distance from axis. Find magnetic field at distance $x$ from axis of wire. Assume $x<R$

which of the following graph correctly represents variation of magnitude of magnetic field $w.r.t.$ distance from axis?

Magnetic field at the centre of a regular hexagonal shaped conductor of side $a,$ carrying current $\mathrm{I},$ is

Magnetic field at a point $(x, y, z)$ is given by $\overrightarrow{B}=\frac{B_{0}y}{{\left(x^2+y^2\right)}^{\frac{1}{2}}}\hat{i}-\frac{B_{0}x}{{\left(x^2+y^2\right)}^{\frac{1}{2}}}\hat{j}.$ Find current enclosed in the loop