A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop i $s ___________$ mV.
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Question

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop i $s ___________$ mV.

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G1 Physics · Accepted Answer

The wire length remains constant while its shape changes. Initial circumference of the circle: L = 2πr = 14π cm. Therefore the side of the square is a = L/4 = 14π/4 = 7π/2 cm. Initial area: A₁ = πr² = 49π cm². Final square area: A₂ = a² = (7π/2)² = 49π²/4 cm². Hence the magnitude of the magnetic-flux change is |ΔΦ| = B|A₂-A₁|. Convert cm² to m²: |ΔΦ| = 0.2 × |49π²/4 - 49π| × 10⁻⁴. Using π ≈ 22/7 gives |ΔΦ| ≈ 6.61×10⁻⁴ Wb. The time interval is Δt = 0.5 s. Therefore, |ε| = |ΔΦ|/Δt = (6.61×10⁻⁴)/0…

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop i s ___________ mV.