Question

A conducting circular loop is placed in a uniform magnetic field of 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mm/s. The induced emf in the loop when the radius is 2cm is:

• A. \(4.8\,\mu\text{V}\)
• B. \(0.8\,\mu\text{V}\)
• C. \(1.6\,\mu\text{V}\)
• D. 3.2μV

Hint:

When area of a loop changes in uniform B: E=B(dA)/(dt)=B(2π r)(dr)/(dt) Always convert mm and cm to SI units.

Answer 1

The Correct Option is C

Step 1: Magnetic flux through the loop: Φ = Bπ r²
Step 2: Induced emf: E = |(dΦ)/(dt)| = B · 2π r · |(dr)/(dt)|
Step 3: Substituting values: B=0.04T, r=2cm=0.02m, (dr)/(dt)=2mm/s=2×10⁻3m/s
Step 4: E =0.04× 2π × 0.02 × 2×10⁻3 ≈ 1.6×10⁻6V ⟹ E=1.6μV