Question

A loop of radius \( R \) carries a current \( I \) and produces a magnetic field \( B \). Which of the following statements is/are correct about \( B \)?

• A. The magnitude of \( B \) is directly proportional to \( I \)
• B. The magnitude of \( B \) is inversely proportional to the square of radius \( R \)
• C. The direction of \( B \) is perpendicular to the plane of the loop
• D. The direction of \( B \) is parallel to the plane of the loop

Hint:

The magnetic field at the center of a current loop is proportional to the current and inversely proportional to the loop radius, and it points perpendicular to the loop.

Answer 1

The Correct Option is A, C

Step 1: Use Biot–Savart law. The magnetic field at the center of a current-carrying loop is given by: \[ B = \frac{\mu_0 I}{2R} \] So, \( B \propto I \) and \( B \propto \frac{1}{R} \), not \( \frac{1}{R^2} \). 
Step 2: Analyze direction. 
The direction of the magnetic field is along the axis of the loop, which is perpendicular to its plane (right-hand rule). 
Step 3: Evaluate options. 
(A) Correct: \( B \propto I \)
(B) Incorrect: Field is inversely proportional to \( R \), not \( R^2 \)
(C) Correct: Field is perpendicular to the loop plane
(D) Incorrect: Field is not in the plane