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

$A$ long cylindrical conductor with a large cross-section carries an electric current distributed uniformly over its cross-section. The magnetic field due to this current is:

What is the magnetic field inside a toroid having $0.1 \ m$ radius and $500$ turns when a current of $0.5 \ A$ is passed through it?

$A$ 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

Consider a circular current-carrying loop of radius $R$ in the $x-y$ plane with its centre at the origin. Consider the line integral $\Im(L) = \left| \int_{-L}^{L} \vec{B} \cdot d\vec{l} \right|$ taken along the $z$-axis.
$(a)$ Show that $\Im(L)$ monotonically increases with $L$.
$(b)$ Use an appropriate Amperian loop to show that $\Im(\infty) = \mu_0 I$,where $I$ is the current in the wire.
$(c)$ Verify this result directly.
$(d)$ Suppose we replace the circular coil with a square coil of side $R$ carrying the same current $I$. What can you say about $\Im(L)$ and $\Im(\infty)$?

$A$ toroid with thick windings of $N$ turns has inner and outer radii $R_{1}$ and $R_{2}$,respectively. If it carries a steady current $I$,the variation of the magnetic field due to the toroid with radial distance $r$ is correctly graphed in