Question

Application of Ampere's Law —

Answer 1

Application of Ampere's Law —

Magnetic field dire to infinitely long straight cylindrical wire :

Magnetic field due to an infinitely long straight cylindrical wire of radius $R$, carrying current $I$ at a point distant $r$ from the axis of the wire is given as follows :

• At a point outside the wire i.e. $(r>R)$ is

$B=\frac{\mu_0 I}{2 \pi r}$

• At a point inside the wire i.e. $(r<R)$ is

$B=\frac{\mu_0 I r}{2 \pi R^2}$

• At a point on the surface of wire i.e. $(r=R)$ is

$B=\frac{\mu_0 I}{2 \pi R}$

The variation of magnetic field $B$ with the distance $r$ from axis is as shown in the figure.

If the cylindrical wire is hollow i.e. it is in the form of pipe, then the magnetic field inside the wire is zero. The variation of magnetic field $B$ with distance $r$ from the axis is as shown in the figure.