(a.) Two parallel plates, each having area A = 3755cm 2 are connected to the ter

Question

(a.)

Two parallel plates, each having area A = 3755cm2 are connected to the terminals of a battery of voltage Vb = 6 V as shown. The plates are separated by a distance d = 0.33cm. You may assume (contrary to the drawing) that the separation between the plates is small compared to a linear dimension of the plate.

1)

A dielectric having dielectric constant = 3 is now inserted in between the plates of the capacitor as shown. The dielectric has area A = 3755 cm2 and thickness equal to half of the separation (= 0.165 cm) . What is the charge on the top plate of this capacitor?

C

2.) What is U, the energy stored in this capacitor?

(b.)

An infiinitely long solid conducting cylindrical shell of radius a = 2.7 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density inner = -0.46 C/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 17 cm, and outer radius c = 19 cm. This conducting shell has a linear charge density outer = 0.46C/m.

1)

What is C, the capacitance of a one meter length of this system of conductors?

HELP PLEASE!

Explanation / Answer

1)

we can assume this as two capacitors connected in series

C1 = epsioon * A/(d/2)

C1 = 8.854 *10^-12 * 3755 *10^-4/(0.0033/2)

C1 = 2.015 *10^-9 F

Now , for the dielectric filled capacitor

C2 = k epsioon * A/(d/2)

C2 = 3*8.854 *10^-12 * 3755 *10^-4/(0.0033/2)

C2 = 6.045 *10^-9 F

Now , the resutatant capacitor is

1/C = 1/2.015 + 1/6.045

C = 1.51 *10^-9 F

charge on the capacitor = 1.51 *10^-9 * 6

charge on the capacitor = 9.07 *10^-9 C

2)

U = 0.5 * CV^2

U = 0.5 * 1.51 *10^-9 * 6^2

U = 2.72 *10^-8 J

the energy stored in the capacitor is 2.72 *10^-8 J

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