A circular magnetic-field region of radius 5 m has uniform B⃗ = 0.25k̂ T. A circular loop of radius 5 m initially covers the region, then moves uniformly at v⃗ = 4î m s⁻¹. Calculate induced emf (V) at t = 2 s. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A circular magnetic-field region of radius 5 m has uniform B⃗ = 0.25k̂ T. A circular loop of radius 5 m initially covers the region, then moves uniformly at v⃗ = 4î m s⁻¹. Calculate induced emf (V) at t = 2 s. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — The field region and moving loop are equal circles of radius R = 5 m; separation of centres at time t is d = vt = 4 × 2 = 8 m. Step 2 — Rate of change of their common area is |dA/dt| = 2√(R²−d²/4) × v. Step 3 — With R = 5 m, d = 8 m: √(25−16) = 3; so |dA/dt| = 2 × 3 × 4 = 24 m² s⁻¹. Step 4 — ε = B|dA/dt| = 0.25 × 24 = 6 V.