Question

1)What is the displacement current through a circular loop of radiusr= 3.00 cm centered on the axis of the capacitor?

2)What is the magnitude of the magnetic field between the capacitor plates at a radiusr= 3.00 cm from the axis of the capacitor?

Answer 1

a)

Displacement current:

I_D = ε₀ ∂φ/∂t

φ = ∫E.dA = E A

E = Q/ε₀A >>>>> φ = (Q/ε₀A) A = Q/ε₀

I_D = ε₀ ∂φ/∂t = dQ/dt = 4 C/s = 4 A

i = I_D (πr²/πR²) = I_D (r²/R²) = 4 * (3*3/(26*26)) = 0.0532544 ≈ 0.0533 A

b)

∫B.dA = μ₀ I_D

>>>> B (2πr) = μ₀ i

>>>> B = (μ₀ i)/2πr

>>>> B = (4*3.1415e-7)*0.0532544/(2*3.14*0.03) = 3.55 * 10^-7 T