Two long straight parallel conductors separated by a distance of $0.5\,m$ carry currents of $5\,A$ and $8\,A$ in the same direction. The force per unit length experienced by each other is
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A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $m$ ' number of turns. It carries a current of $5 \mathrm{~A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$, then the value of $m$ is :
A long straight wire is carrying current $I_1$ in $+z$ direction. The $x-y$ plane contains a closed circular loop carrying current $I_2$ and not encircling the straight wire. The force on the loop will be:
A galvanometer coil has $500$ turns and each turn has an average area of $3 \times 10^{-4}\, m ^{2}$. If a torque of $1.5\,Nm$ is required to keep this coil parallel to magnetic field when a current of $0.5\, A$ is flowing through it, the strength of the field (in $T )$ is
A semicircular ring of radius $R$ carrying current $i$ is placed in a magnetic field of intensity $B$ so that plane of wire is perpendicular to magnetic field as shown. Net force acting on the ring is
An infinitely long wire, located on the $z$-axis, carries a current $/$ along the $+z$-direction and produces the magnetic field $\vec{B}$. The magnitude of the line integral $\int \vec{B} \cdot d l$ along a straight line from the point $(-\sqrt{3} a, a, 0)$ to $(a, a, 0)$ is given by [ $\mu_0$ is the magnetic permeability of free space.]