1. Consider the capacitive circuit shown below:
a) Calculate the total equivalent capacitance for this circuit.
b) What is the total amount of charge provided by the voltage source when the capacitors are fully charged?
c) How much energy has been provided by the battery?
2. Shown below are two lines of charge bent into concentric
rings. The outer ring has a linear charge density of +l (C/m) and radius R while the inner ring has a charge density - l (C/m) radius R/2. 
a) Find the electric potential at a point P a distance of 2R along the x-axis due to the charge distribution if the potential infinitely far away is zero.
b) What is the change in potential energy which results from moving a charge qo from x= 2 R to x= R.
3. One kind of coaxial capacitor consists of two concentric cylindrical shells in the geometry shown below. Answer the following questions based on the capacitor below. Your answer should be expressed in terms of the the dimensions shown in the diagram below and physical quantities which are given in the problem.
a) Calculate the capacitance for this set of conducting shells.
b) A material with a dielectric constant of k=2 is placed in the space between the conductors and a charge of +Qo and -Qo is placed on the cylinders. Explain what will happen to the electric field in between the shells .
c) Calculate the electrostatic energy stored in the capacitor if it is charged as described in b) above.
4. Consider the capacitive circuit shown below:
V
a) Calculate the total equivalent capacitance for this circuit.
b) What is the total amount of charge provided by the voltage source when the capacitors are fully charged?
c) How much energy is provided by the battery to the circuit?
5. Consider two long straight parallel wires of length L and diameter 2a which are separated by a distance d.
a) Calculate the capacitance for this arrangement of conductors.
b) If a 12 V battery is hooked up to the two wires, then how much charge develops on each of the wires?
c) How much energy is stored by the capacitor when it is connected to the 12 V battery
d) If the two fully charged wires are placed in a liquid with a dielectric constant of k=4, then briefly explain what will happen to the electric field between the wires and why.
6. Shown below is a line of charge bent into a semicircular annular ring of radius R=0.05 m which is lying in the y-z plane. The ring has a total charge of Q=5.0x10-6 C uniformly distributed along its length.
a) Find the electric potential at a point P a distance of 0.01 m from the origin if the potential infinitely far away is defined as zero.
b) Find the electric potential at the origin.
c) How much work must be done to move a Helium nucleus ( of charge +2e, twice the charge of a proton) from x=0.1 m to the origin? (e=1.6x10-19 C)
7. 
Three
point charges are placed as shown in the coordinate system below.
8.
a) Calculate the electric potential at the origin by assuming the potential infinitely far away is zero.
b) Calculate the potential at (x=10m, y=9m).
c) How much energy is required to move a charge of 1x10-6 C from the origin to (x=5m,y=3m)?
d) How much energy does it take to move an electron (charge e-=1.6x10-19C ) from x=¥ to the origin?
9. Consider the below capacitive circuit.
24V
a) Find the equivalent capacitance for this circuit.
b) How much total charge is provided to the circuit by the battery?
c) What is the charge which accumulates on the 8 mF capacitor?
d) Calculate the potential difference across the 8 mF capacitor.
e) How much energy is stored by the 6 mF capacitor which is in series with the 8mF cap?
f) How much energy is stored by the entire circuit? That is, how much energy does the battery provide?
9.Consider the coaxial cylindrical arrangement of conductors shown below.
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