A circular parallel-plate capacitor of radius 0.10 m is charged by a current of 2 A. Assuming a uniform electric field between the plates, find the magnetic field at r = 0.05 m from the axis. If B = N×10⁻⁶ T, find N. Take μ₀ = 4π×10⁻⁷ T·m/A.
Physics · Electromagnetic wave · displacement current and properties of electromagnetic wave
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Question

A circular parallel-plate capacitor of radius 0.10 m is charged by a current of 2 A. Assuming a uniform electric field between the plates, find the magnetic field at r = 0.05 m from the axis. If B = N×10⁻⁶ T, find N. Take μ₀ = 4π×10⁻⁷ T·m/A.

Physics · Electromagnetic wave · displacement current and properties of electromagnetic wave

G1 Physics · Accepted Answer

For r<R, the enclosed displacement current is I(enclosed) = I(r²/R²). Here, I = 2 A, r = 0.05 m, R = 0.10 m. Thus, I(enclosed) = 2(0.05²/0.10²) = 0.5 A. Ampere-Maxwell law gives B(2πr) = μ₀I(enclosed). Therefore, B = μ₀I(enclosed)/(2πr) = (4π×10⁻⁷)(0.5)/[2π(0.05)] = 2×10⁻⁶ T. Hence N = 2.