The magnetic field $B$ within a solenoid having $n$ turns per meter length and carrying a current of $i$ amperes is given by:

$A$ solenoid has a core of a material with relative permeability $400$. The windings of the solenoid are insulated from the core and carry a current of $4 \,A$. If the number of turns is $500$ per metre,then the magnetizing field is

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 $.........A$.

In the following diagram,there is a straight wire carrying a current $I$. Consider a circular path with radius $R$ near it. If $\vec{B}_T$ is the tangential component of the magnetic field along the circular path,then find the value of the integral $\oint \vec{B}_T \cdot d\vec{l}$.

$A$ long solenoid is formed by winding $20$ $turns/cm$. The current necessary to produce a magnetic field of $20$ $mT$ inside the solenoid will be approximately ..... $A$ $(\frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A})$.

$A$ solenoid has a turn density of $5000 \, \text{turns/m}$ and a cross-sectional area of $10 \, \text{cm}^2$. If a current of $1 \, \text{A}$ flows through it and the core material has a relative permeability of $1000$, find the energy per unit length of the solenoid in $\text{J/m}$.