Question

An infinite long wire lying along the $Y$-axis, is carrying a current $I$ as shown in the figure. The magnetic flux through a circular loop of radius $R$ in the $XY$ - plane is
[Assume ${\mu }_0=$ magnetic in tree space permeability

• A. $\frac{{\mu }_{0}I}{2\pi R}$
• B. ${\mu }_{0}IR$
• C. $\frac{{\mu }_{0}I}{\pi R^2}$
• D. ${\mu }_{0}I\pi R^2$
• E. None of the above

Answer 1

Answer: (E)

The magnetic field at point due to a current carrying straight conductor of infinite length is

The magnetic flux through circular loop around conductor in $xy$-plane is ${\varphi }_B=BA=\frac{{\mu }_{0}I}{2\pi R}\times \pi R^2$
$=\frac{{\mu }_{0}IR}{2}$