$A$ solenoid of length $0.5 \ m$ has a radius of $1 \ cm$ and is made up of $250$ turns. It carries a current of $5 \ A$. What is the magnitude of the magnetic field inside the solenoid?

$A$ solenoid of $1000$ turns per metre has a core of material with relative permeability $400$. The windings of the solenoid are insulated from the core and a current of $2 \ A$ is passed through the solenoid. Then the value of the magnetic intensity inside the solenoid is

$A$ solenoid $2 \,m$ long and $4 \,cm$ in diameter has $4$ layers of windings of $1000$ turns each and carries a current of $5 \,A$. What is the magnetic field at its centre along the axis? $\left[\mu_0=4 \pi \times 10^{-7} \,Wb / Am\right]$

What current must be passed through a solenoid with $20 \text{ turns/cm}$ to produce a magnetic field of $20 \text{ mT}$ (in $\text{ A}$)? (Given: $\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A}$)

$A$ long wire carrying a current of $18 \,A$ is kept along the axis of a long solenoid of radius $1 \,cm$. The magnetic field due to the solenoid is $8.0 \times 10^{-3} \,T$. The magnitude of the resultant magnetic field at a point $0.6 \,mm$ from the solenoid axis is (Assume $\mu_0 = 4 \pi \times 10^{-7} \,Tm/A$):

Two wires carrying currents of $5 \ A$ and $2 \ A$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $3 \ A$ is situated outside the loop. The value of $\oint \overrightarrow{B} \cdot d\overrightarrow{l}$ around the loop is ($\mu_0 = \text{permeability of free space}$,$d\overrightarrow{l}$ is the length element of the Amperian loop).