$A$ solenoid is $1 \ m$ long and $4 \ cm$ in diameter. It has five layers of windings of $1000$ turns each and carries a current of $7 \ A$. The magnetic field at the centre of the solenoid is

$A$ 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 $\text{J/m}$.

$A$ closely wound solenoid of $80 \,cm$ long has $5$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8 \,cm$. If the current carried is $8 \,A$, then the magnitude of the magnetic field inside the solenoid near its centre is approximately

$A$ 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

$A$ steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement$(s)$ is (are) :
$(A)$ In the region $0 < r < R$,the magnetic field is non-zero.
$(B)$ In the region $R < r < 2R$,the magnetic field is along the common axis.
$(C)$ In the region $R < r < 2R$,the magnetic field is tangential to the circle of radius $r$,centered on the axis.
$(D)$ In the region $r > 2R$,the magnetic field is non-zero.

Assertion: The magnetic field produced by a current-carrying solenoid is independent of its length and cross-sectional area.
Reason: The magnetic field inside the solenoid is uniform.