Concept #1: Intro To Dielectrics

Example #1: Charge After Inserting Dielectric

Practice: A parallel plate capacitor is formed by bringing two circular plates, of radius 0.5 cm, to a distance of 2 mm apart. The capacitor is made so that it has a dielectric of constant between the plates. When the charge on the capacitor is 3 nC, the voltage of the capacitor is 5000 V. What is the dielectric constant?

Example #2: Partial Dielectrics

A parallel plate capacitor has a measured capacitance of 1.0 pF, and is charged to 2.0 μC, then disconnected from the power supply. The space between the plates is then filled with a certain dielectric material with a dielectric constant of K = 4.0. What is the resulting capacitance and the stored electric potential energy?
A) 4.0 pF and 1.0 J
B) 0.25 pF and 0.5 J
C) 4.0 pF and 0.5 J
D) 4.0 pF and 4.0 J

The figure below shows four parallel plate capacitors: A, B, C, and D. Each capacitor carries the same charge q and has the same plate area A. As suggested by the figure, the plates of capacitor A and C are separated by a distance d while those of B and D are separated by a distance 2d. Capacitors A and B are maintained in vacuum while capacitors C and D contain dieelctrics with constant k = 5. Which list below places the capacitors in order of increasing capacitance?
A) A, B, C, D
B) B, A, C, D
C) A, B, D, C
D) B, A, D, C
E) D, C, B, A

A parallel-plate capacitor is connected to a battery and allowed to charge up. While still connected to battery, a dielectric material is then inserted between two plates of the capacitor. What can we say about the new charges on the capacitor plates?
A) The total charges increases
B) The total charges decreases
C) The total charges remains the same
D) Unable to determine from the information given

A parallel plate capacitor has plates with area A = 350cm2 separated by a distance d = 1.5mm. A dielectric with dielectric constant K = 3.1 is inserted between the two plates. What is the capacitance now?

A stack of paper with net dielectric constant K is placed between the plates of a capacitor holding a fixed charge. What happens to the electric field F and the energy U stored between the plates (E0 and U0 are the values before sheet is inserted)?
A. E → E0/K, U → U0/K
B. E → E0/K, U → U0K
C. E → E0K, U → U0K
D. E → E0K, U → U0/K
E. E → E0, U → U0/K2

The effective area of each plate of parallel plate capacitor is 2.1 m2. The capacitor is filled with neoprene rubber (k = 6.4). When a 6.0-V potential difference exists across the plates of the capacitor stores 4.0 µC of charge. Determine the plate separation of capacitor.