3. Capacitance and dielectrics

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8

The potential difference between the plates of a 3μF capacitor is 100 V. How much energy is stored in the capacitor?

U = 15 mJ

How many 1μF capacitors connected in parallel would it take to store a total charge of 1 mC if the potential difference of across each capacitor is 10 V?

n = 100

C = 2.72 nF

You are a laboratory assistant in a physics department that has budget problems. Your supervisor wants to construct cheap parallel-plate capacitors for use in introductory laboratory experiments. The design uses polyethylene, which has a dielectric constant of 2.3, between two sheets of aluminum foil. The area of each sheet of foil is 400 cm2 and the thickness of the polyethylene is 0.3 mm. Find the capacitance of this arrangement (ε0 = 8.85 ✕ 10-12 C2/N.m2).

17

The positively charge plate of a parallel-plate capacitor has a charge equal to Q. When the space between the plates is evacuated of air, the electric field strength between the plates is 2.5 × 105 V/m. When the space is filled with a certain dielectric material, the field strength between the plates is reduced to 1.2 × 105 V/m. (a) What is the dielectric constant of the material? (b) If Q = 10 nC, what is the area of the plates? (c) What is the total induced bound charge on either face of the dielectric material?

K = 2.1; A = 45 cm2; Qind = 5.2 nC;

18

A spherical capacitor contains a charge of 3.3 nC when connected to a potential difference of 230 V. If its plates are separated by vacuum and the inner radius of the outer shell is 4.6 cm. Calculate its capacitance and its inner radius.

C = 14.3 pF, a= 3.4 cm

A coaxial cable from a television has a diameter of the inner conductor and the diameter of the shield are 1 and 5 mm, respectively. The dielectric constant of the dielectric separating the two conductors is K = 3. Determine the capacitance per unit length of the cable.

C/L = 0.1 nF/m