A circular parallel-plate capacitor of plate radius R is being charged by a constant current I. Assuming a uniform electric field between the plates, the magnetic field at a distance r < R from the axis is:
Options

Question

A circular parallel-plate capacitor of plate radius R is being charged by a constant current I. Assuming a uniform electric field between the plates, the magnetic field at a distance r < R from the axis is:

Options

G1 Physics · Accepted Answer

Apply the Ampere-Maxwell law to a circular Amperian loop of radius r between the plates: ∮B·dl = μ₀ × (enclosed displacement current). Because the electric field is uniform, the displacement-current density is uniform over the circular plate area. Total plate area = πR². Area enclosed by the loop = πr². Therefore, enclosed displacement current = I(πr²/πR²) = I(r²/R²). Hence, B(2πr) = μ₀I(r²/R²). Therefore, B = μ₀Ir/(2πR²). Correct option: B.