$A$ hollow cylinder of infinite length carries a uniform current per unit length $\lambda$ along its circumference,as shown. The magnetic field inside the cylinder is:

Two coaxial solenoids $1$ and $2$ of the same length are placed such that one is inside the other. The number of turns per unit length are ${n_1}$ and ${n_2}$. The currents ${i_1}$ and ${i_2}$ are flowing in opposite directions. The magnetic field inside the inner coil is zero. This is possible when:

$A$ long solenoid is fabricated by closely winding a wire of radius $0.5 \, mm$ over a cylindrical frame so that the successive turns nearly touch each other. What is the magnetic field at the centre of the solenoid if it carries a current of $5 \, A$?

The region inside a current-carrying toroid is filled with a material (Niobium) having magnetic susceptibility $\chi = 2.6 \times 10^{-5}$. The percentage increase in the magnetic field in the presence of Niobium over that without it is:

$A$ current of $1/4\pi \ A$ is flowing through a toroid. It has $1000$ turns per meter. The value of the magnetic field (in $Wb/m^2$) along its axis is:

Current is flowing through a conducting hollow pipe whose cross-section is shown in the figure. The value of magnetic induction will be zero at: