Question

A long straight wire of a circular cross section (radius $a$ ) carries a steady current $I$ and the current $I$ is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field $B$ with distance $r$ from the centre of the wire?

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Magnetic field due to a long straight wire of radius $a$ carrying current $I$ at a point distant $r$ from the centre of the wire is given as follows:
$B=\frac{{\mu }_{0}Ir}{2\pi a^2}$ for $r<a$
$B=\frac{{\mu }_{0}I}{2\pi a}$ for $r=a$
$B=\frac{{\mu }_{0}I}{2\pi r}$ for $r>a$

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