Question

A cylindrical wire of radius R carries a current directed out of the page as shown below. The current has a constant cross-sectional area density J. According to Ampere's Law, the current creates magnetic field both within the wire and outside the wire.
What current is enclosed in a circular loop that is centered on the wire's axis and has a radius $r>R$?

• A. $\frac{\pi J{R}^3}{3}$
• B. $\pi J{R}^2$
• C. $4\pi J{R}^2$
• D. $2\pi JR$
• E. $\pi J{R}^3$

Answer 1

Answer: (B)

$\pi J{R}^2$

Current enclosed by the loop of radius $r>R$ is equal to the total current flowing through the wire.

Cross-sectional area of the wire $A=\pi R^2$

$\therefore$ Current enclosed by the loop of radius $r>R$, $I=JA=J\left(\pi R^2\right)=\pi J{R}^2$