1. Consider scenario A in which a pair of irregular plates with area A and separ

Question

1. Consider scenario A in which a pair of irregular plates with area A and separation D that act as a capacitor, are connected to the battery with potential difference V0. Ignore fringe effects.

(a) What is the condition under which this system behaves like an ideal parallel-plate capacitor? Express the relation in terms of A and D.

(b) Derive the formula for capacitance for the parallel-plate configuration.

(c) Find the capacitance if A = (1 cm)^2 , D = 1 mm, and V0 = 10 V .

2. Consider a scenario B: After scenario A, the capacitor is disconnected and the plates are separated by external force, keeping the charges constant, until the separation is 2D. Express the answers symbolically using some or all of the following symbols: A, D, 0, and V0.

(a) Write the expression for the potential difference.

(b) Write the expression for the initial and final stored energy in the capacitor.

(c) Write the expression for the work required by the external force to move the plates from D to 2D.

3. Now consider a cylindrical capacitor. Show that under the condition expressed in Problem 1a above, the cylindrical capacitor looks like a parallel plate capacitor.

(a) Rewrite the capacitance by expressing the larger radius as b = a + .

(b) Expand the capacitance to O() given that /a <<1.

Explanation / Answer

1.

a)

here

Q = C * V

C = e0 * A / D

C is the capacitance and Q is the charge and V is the voltage

b)

the capacitance of parallel plate capacitor is

C = e0 * A / D

c)

use the same formula for the capacitance

C = 8.854 * 10^-12 * 1 * 10^-4 / 10^-3

C = 8.854 * 10^-13 F

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