The magnetic field at point $P$ in the given figure, due to a current $I$ flowing through a cylindrical conductor of radius $R$, is:

$A$ solenoid has $N$ turns,length $l$,and cross-sectional radius $r$. If a current $i$ flows through the solenoid,what is the magnetic field at the axial midpoint? (Given $l \simeq r$)

$A$ current $I$ flows along the length of an infinitely long,straight and thin-walled pipe. Then

The magnetic flux near the axis and inside the air core solenoid of length $60 \, cm$ carrying current '$I$' is $1.57 \times 10^{-6} \, Wb$. Its magnetic moment will be $[\mu_0 = 4 \pi \times 10^{-7} \, SI \, unit$ and cross-sectional area is very small as compared to the length of the solenoid.] (in $Am^2$)

$A$ closely wound solenoid of $1200$ turns and area of cross-section $5 \,cm^2$ carries a current. If the magnetic moment of the solenoid is $1.2 \,J \,T^{-1}$, then the current through the solenoid is (in $\,A$)

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: