$A$ $50 \ cm$ long solenoid has a winding of $400$ turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \ T$ at the centre (in $A$)?

An imaginary north pole of $10 \, Am$ is rotating around an infinitely long current-carrying wire at $30 \, \text{revolutions/min}$ on a circular path. If the current in the wire is $5 \, A$, then calculate the work done in one second.

$A$ closely wound solenoid of length $1 \,m$ has $5$ layers of $500$ turns each. If the magnitude of the magnetic field inside the solenoid near its centre is $4.4 \,mT$, the current carried is: (in $\,A$)

Write the equation for the magnetic field at an inside point of a very long solenoid.

$A$ solenoid has $N$ turns,length $l$,and cross-sectional radius $r$. If a current $i$ flows through the solenoid,what is the magnetic field at the axial midpoint? (Given $l \simeq r$)

$A$ toroid with thick windings of $N$ turns has inner and outer radii $R_{1}$ and $R_{2}$,respectively. If it carries a steady current $I$,the variation of the magnetic field due to the toroid with radial distance $r$ is correctly graphed in