$A$ solenoid of length $0.25 \ m$ has a radius of $1 \ cm$ and is made up of $500$ turns. It carries a current of $2.5 \ A$. What is the magnitude of the magnetic field inside the solenoid? (Take $\mu_0 = 4 \pi \times 10^{-7} \ SI$ units).

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:

$A$ magnetic field of $100 \;G$ $(1 \;G = 10^{-4} \;T)$ is required which is uniform in a region of linear dimension about $10 \;cm$ and area of cross-section about $10^{-3} \;m^2$. The maximum current-carrying capacity of a given coil of wire is $15 \;A$ and the number of turns per unit length that can be wound round a core is at most $1000 \;turns \;m^{-1}$. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

The current required to be passed through a solenoid of $15\,cm$ length and $60$ turns in order to demagnetize a bar magnet of magnetic intensity $2.4 \times 10^3\,A/m$ is $.........A$.

The figure shows the cross-sectional view of a hollow cylindrical conductor with inner radius $R$ and outer radius $2R$,carrying a uniformly distributed current $i$ along its axis. The magnetic induction at point $P$ at a distance $3R/2$ from the axis of the cylinder will be

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: