Question

A conducting square loop is placed in a magnetic field \(B\) with its plane perpendicular to the field. The sides of the loop are shrinking at a constant rate \(\alpha\). The induced emf in the loop at an instant when its side is \(a\) is:

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

Hint:

For changing area in uniform magnetic field: \[ \mathcal{E} = B\frac{dA}{dt} \] Use absolute value for magnitude.

Answer 1

The Correct Option is A

Step 1: Magnetic flux through the loop: \[ \Phi = Ba^2 \]
Step 2: Induced emf: \[ \mathcal{E} = \left|\frac{d\Phi}{dt}\right| \]
Step 3: Since \(\frac{da}{dt} = -\alpha\): \[ \mathcal{E} = B \cdot 2a \cdot \alpha \]