3. A parallel-plate capacitor is made of two identical circular plates of diamet

Question

3. A parallel-plate capacitor is made of two identical circular plates of diameter 3 mm. The distance between the plates is 1 mm. a) Find the capacitance of this capacitor. b) If this capacitor is connected to a 4 V battery, what will be the electric charge in each plate? c) If we reverse the orientation of the battery (relative to the orientation in (b)), what difference is there in the charges of the capacitor plates, compared to (b)? (Is the magnitude of the charges the same? Are the signs of the charges the same?) d) Compute the electric field between the plates. To do this, model the capacitor as an infinite plate capacitor. Draw the capacitor and the electric field lines. Make sure you indicate the direction of the electric field lines. How much electric energy is stored in this capacitor?

Explanation / Answer

3)

a) C = A*epsilon/d

= pi*(0.003/2)^2*8.854*10^-12/(1*10^-3)

= 6.26*10^-14 F

b) Q = C*V

= 6.26*10^-14*4

= 3.50*10^-13 C

c) magnitude of the charges the same.

d) E = V/d

= 4/(1*10^-3)

= 4*10^3 N/c or V/m

e) U = (1/2)*C*V^2

= (1/2)*6.26*10^-14*4^2

= 5.01*10^-13 J

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