Question

A current \( I \) flows in the anticlockwise direction through a square loop of side \( a \) lying in the \( xoy \)-plane with its center at the origin. The magnetic induction at the center of the square loop is given by

• A. \( \frac{2 \mu_0 I}{\pi a^2} \hat{e}_x \)
• B. \( \frac{2 \mu_0 I}{\pi a^2} \hat{e}_y \)
• C. \( \frac{2 \mu_0 I}{\pi a^2} \hat{e}_z \)
• D. \( \frac{2 \mu_0 I}{\pi a^2} \hat{e}_x \)

Hint:

The magnetic field at the center of a current-carrying square loop is directed along the axis perpendicular to the plane of the loop.

Answer 1

The Correct Option is C

Step 1: Magnetic Field at the Center of the Loop.
For a current-carrying square loop, the magnetic field at the center of the loop is given by: \[ B = \frac{2 \mu_0 I}{\pi a^2} \] where \( a \) is the side length of the square. The direction of the magnetic field is along the \( z \)-axis due to the symmetry of the loop.
Step 2: Conclusion.
The correct answer is (C), \( \frac{2 \mu_0 I}{\pi a^2} \hat{e}_z \).