Question

A current carrying infinite wire is passing through the centre of a ring of radius $R$ and perpendicular to plane of the ring. The magnetic flux passing through the ring will be

• A. $\frac{\mu_0 IR}{4}$
• B. $\frac{\mu_0 IR}{2}$
• C. $\mu_0 IR$
• D. Zero

Answer 1

Answer: (D)

Zero

Answer 2

The wire is along the center and perpendicular to the plane of the ring, so if the ring lies in the xy-plane, the wire is along the z-axis.

The magnetic field $\vec{B}$ due to a long straight wire is given by

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

and is directed tangentially (circles around the wire).

Since the ring's area vector ($\vec{A}$) points along the z-axis while the magnetic field is tangential in the xy-plane, the dot product $\vec{B} \cdot \vec{A} = 0$ at every point.

Therefore, the net magnetic flux through the ring is zero.