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 $x y$-plane is [assume, $\mu_0=$ magnetic in free space permeability]

• A

  $\frac{\mu_0 l}{2 \pi R}$
• B

  $\mu_0 / R$
• C

  $\frac{\mu_0 l}{\pi R^2}$
• Correct answer
  D

  None of these

Solution

The magnetic field at point due to a current carrying straight conductor of infinite length is
$B=\frac{\mu_0 I}{2 \pi R}$ The magnetic flux through circular loop around conductor in $x y$-plane is $\phi_B=B A=\frac{\mu_0 I}{2 \pi R} \times \pi R^2=\frac{\mu_0 I R}{2}$

Hence, the correct answer is option: 'D'.