Ampere’s Law

Two current carrying wire of infinite length are placed perpendicular to $x$-$y$ plane at $x=0$ and $x=R\sqrt{3}$ as shown in figure. Current in both the wires is same and inwards to the $x$-$y$ plane. Find ratio of $\left|\int \overrightarrow{B}·\mathrm{d}\overrightarrow{l}\right|$ in segment $CDA$ to segment $ABC$ will be :

A steady electric current is flowing through a cylindrical conductor.

A long, straight wire of radius $R$ carries a current distributed uniformly over its cross section. The magnitude of the magnetic field is

Two identical current carrying co-axial loops, carry current $I$ in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as $C$

Three distinct current carrying wires intersect a finite rectangular plane $ABCD$. The current in the left wire and the loop is $I_1$. The direction of current in left-most wire and right-most loop is downwards as shown in the figure. The current $I_2$ through the middle wire is adjusted so that the path integral of the total magnetic field along the perimeter of the rectangle is zero, that is, ${\oint }_{\mathrm{ABCDA}}\overrightarrow{\mathrm{B}}·\overrightarrow{\mathrm{dl}}=0.$ Then the current $I_2$ 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 figure shows a long coaxial cable in which a current $I$ flows down through the inner cylinder of radius $a$ and the same current flows back up through the outer cylinder of radius $2a$. The cylinders are insulated from each other and the current is uniformly distributed over the area of the cross-section in each cylinder. The strength of the magnetic field at a distance $\raisebox{1ex}{$3a$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ from the axis of the cable is

A long straight wire carrying a current of $30\mathrm{ }\mathrm{A}$ is placed in an external uniform magnetic field of induction $4\times {10}^{–4}\mathrm{ }\mathrm{T}$ . The direction of external magnetic field is along the direction of the current. The magnitude of the resultant magnetic induction at a point $2.0\mathrm{ }\mathrm{c}\mathrm{m}$ away from the wire is $n\times {10}^{-4} \mathrm{T}$. What is the value of $n$?