A 3.0 cm diameter parallel plate capacitor with 1.0 mm spacing is being charged

Question

A 3.0 cm diameter parallel plate capacitor with 1.0 mm spacing is being charged at a rate of .80 C/s.
a. Find the strength of the magnetic field at a distance of 1 cm from the axis of the capacitor.
b. The capacitor is connected to a 12 V battery. What is the energy density inside the capacitor after it is fully charged? A 3.0 cm diameter parallel plate capacitor with 1.0 mm spacing is being charged at a rate of .80 C/s.
a. Find the strength of the magnetic field at a distance of 1 cm from the axis of the capacitor.
b. The capacitor is connected to a 12 V battery. What is the energy density inside the capacitor after it is fully charged?
a. Find the strength of the magnetic field at a distance of 1 cm from the axis of the capacitor.
a. Find the strength of the magnetic field at a distance of 1 cm from the axis of the capacitor.
b. The capacitor is connected to a 12 V battery. What is the energy density inside the capacitor after it is fully charged?

Explanation / Answer

(a).
  
displacement current, Id = 80 C/s = 80 A

applying Ampere's law,

B . L = u0 Id

B ( 2 pi 0.01) = (4pi x 10^-7) ( 80)

B = 1.6 x 10^-3 T

(B) C = e0 A / d

C = (8.854 x 10^-12) ( pi * 0.015^2) / (1 x 10^-3)

C = 6.26 x 10^12 F

energy stored = C V^2 / 2 = (6.26 x 10^-12) (12^2) / 2 = 4.506 x 10^-10 J

energy density = U / volume = (4.506 x 10^-10) / (pi * 0.015^2 x 0.001)

= 6.375 x 10^-4 J/m^3

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