A uniform magnetic field B exists perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB/dt = 0.032 T s⁻¹. The induced current in the loop is close to (Resistivity of the…

Question

A uniform magnetic field B exists perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB/dt = 0.032 T s⁻¹. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 × 10⁻⁸ Ω m)

Accepted Answer

(2) 0.61 A. The wire is 30 cm long, so the square has side 7.5 cm and A=5.625×10⁻³ m². ε=A(dB)/(dt)=5.625×10⁻³×0.032=1.8×10⁻⁴ V. Wire cross-section: a=π(2×10⁻³)²=1.257×10⁻⁵ m², so R=(ρ L)/a=(1.23×10⁻⁸×0.3)/(1.257×10⁻⁵)=2.94×10⁻⁴ Ω. I=(1.8×10⁻⁴)/(2.94×10⁻⁴)=0.61 A.

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