Question

A conducting square loop is placed in a magnetic field B with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate α. The induced emf in the loop at the instant when its side is a is

• A. \( 2\alpha a B \)
• B. \( \alpha^2 a B \)
• C. \( 2\alpha^2 a B \)
• D. α a B

Hint:

Always express magnetic flux in terms of area for deforming loops.

Answer 1

The Correct Option is A

Step 1: Area of square loop: A = a²
Step 2: Rate of change of area: (dA)/(dt) = 2a(da)/(dt) = -2aα
Step 3: Induced emf: E = B|(dA)/(dt)| = 2α a B