This document contains 29 multi-part physics problems related to electric fields, electric potential, and capacitance. The problems cover a range of concepts including Gauss's law, electric fields due to various charge distributions, capacitors in series and parallel, energy stored in capacitors, and more. Detailed calculations and explanations are required to fully solve each problem.

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School of Applied Natural Sciences, Applied Physics Department
General physics II #worksheet I
1. A point charge causes an electric flux of -750 N. m2
/C to pass through a spherical
Gaussian surface of 10cm radius centered on the charge. (a) If the radius of the Gaussian
surface were doubled, how much flux would pass through the surface? (b) What is the
value of the point charge?
2. An infinitely long insulating cylinder of radius R has a volume charge density that varies
with the radius as
where , a, and b are positive constants and r is the distance from the axis of the
Cylinder. Use Gauss’s law to determine the magnitude of the electric field at radial a
distances (a) r < R and (b) r >R.
3. Eight point charges, each of magnitude q, are located on the corners of a cube of side s,
as shown in Figure (a) Determine the x, y, and z components of the resultant force exerted
on the charge located at point A by the other charges. (b) What are the magnitude and
direction of this resultant force?
4. Charge Q is uniformly distributed in a sphere of radius R. (a) What fraction of the charge
is contained within radius r= R/2? (b) What is the ratio of the electric field magnitude at
r= R/2 to that on the surface of the sphere?
5. The electric field in a particular space is E= (x + 2)i N/C, with x in meters. Consider a
cylindrical Gaussian surface of radius 20cm that is coaxial with the x axis. One end of the
cylinder is at x = 0. (a) What is the magnitude of the electric flux through the other end of
the cylinder at x=2.0 m? (b) What net charge is enclosed within the cylinder?
6. The following figure shows, in cross section, two solid spheres with uniformly distributed
charge throughout their volumes. Each has radius R. Point P lies on a line connecting the
centers of the spheres, at radial distance R/2 from the center of sphere 1.If the net electric
field at point P is zero, what is the ratio q2/q1 of the total charge q2 in sphere 2 to the total
charge q1 in sphere 1?
7. Two charged spheres are 8cm apart. They are moved closer to each other enough that the
force on each of them increases four times. How far apart are they now?

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8. Two initially uncharged identical metal spheres, 1 and 2, are connected by an insulating
spring (unstretched length L0 = 1.00 m, spring constant k = 25.0 N/m), as shown in the
figure. Charges +q and –q are then placed on the spheres, and the spring contracts to
length L = 0.635 m. Determine the charge q. If the spring is coated with metal to make it
conducting, what is the new length of the spring?
9. The figure shows a uniformly charged thin rod of length L that has total charge Q. Find
an expression for the magnitude of the electrostatic force acting on an electron positioned
on the axis of the rod at a distance d from the midpoint of the rod
10. A solid conducting sphere of radius r1 has a total charge of +3Q. It is placed inside (and
concentric with) a conducting spherical shell of inner radius r2 and outer radius r3. Find
the electric field in these regions: r < r1, r1 < r < r2, r2 < r < r3, and r > r3.
11. Consider an electric dipole on the x-axis and centered at the origin. At a distance h along
the positive x-axis, the magnitude of electric field due to the electric dipole is given by
k(2qd)/h3
. Find a distance perpendicular to the x-axis and measured from the origin at
which the magnitude of the electric field stays the same.
12. Two point charges are placed at two of the corners of a triangle as shown in the figure.
Find the magnitude and the direction of the electric field at the third corner of the
triangle.
13. Four charges of equal magnitude are arranged at the corners of a square of side L as shown
in Figure (a) Find the magnitude and direction of the force exerted on the charge in the
lower left corner by the other charges. (b) Show that the electric field at the midpoint of
one of the sides of the square is directed along that side toward the negative charge and has
a magnitude E given by 80
14. A thin glass rod is bent into a semicircle of radius R. A charge +Q is uniformly
distributed along the upper half, and a charge –Q is uniformly distributed along the lower

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half as shown in the figure. Find the magnitude and direction of the electric field 𝐸⃗ (in
component form) at point P, the center of the semicircle.
15. In the following figure, particle 1 of charge q1=+e and particle 2 of charge q2=-5e are
fixed on an x axis. Distance d =5.60μm.What is the electric potential difference VA - VB?
16. In one model, a proton is considered to be a spherical ball of charge of uniform volume
charge density with radius R and total charge Q. Find the potential V inside and derived
the expression for potential outside of the sphere can be,
17. The plastic rod of length L shown in the figure has the nonuniform linear charge
distribution λ = cx, where c is a positive constant. Find an expression for the electric
potential at point P on the y-axis, a distance y from one end of the rod.
18. Derive an expression for electric potential along the axis (the x-axis) of a disk with a hole
in the center, as shown in the figure, where R1 and R2 are the inner and outer radii of the
disk. What would the potential be if R1 = 0?
19. The electric field, 𝐸⃗ (𝑟) , and the electric potential, 𝑉(𝑟), are calculated from the charge
distribution, 𝜌(𝑟) by integrating Coulomb’s Law and then the electric field. In the other
direction, the field and the charge distribution are determined from the potential by suitably
differentiating. Suppose the electric potential in a large region of space is given by V(r) =
V0exp (r2
/a2
), where V0 and a are constants and 𝑟 = √𝑥2 + 𝑦2 + 𝑧2 is the distance from
the origin. a) Find the electric field 𝐸⃗ (𝑟) in this region. b) Determine the charge density
𝜌(𝑟) in this region, which gives rise to the potential and field. c) Find the total charge in
this region. d) Roughly sketch the charge distribution that could give rise to such an electric
field.
20. An electron is accelerated horizontally from rest by a potential difference of 2200 V It
then passes between two horizontal plates 6 5 cm long and 1 3 cm apart that have a

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potential difference of 250 V . At what angle 𝜃 will the electron be traveling after it
passes between the plates?
21. The switch S in Fig. is connected downward so that capacitor C2 becomes fully charged
by the battery of voltage V0 If the switch is then connected upward, determine the charge
on each capacitor after the switching
22. In the circuit shown in Fig, C1 = 1.0 𝜇F, C2 = 2𝜇F, C3 = 2.4 𝜇F and a voltage ∆𝑉 = 24 V
is applied across points a and b. After C1 is fully charged, the switch is thrown to the
right. What is the final charge and potential difference on each capacitor?
23. A 175-pF capacitor is connected in series with an unknown capacitor, and as a series
combination they are connected to a 25.0-V battery. If the 175-pF capacitor stores 125 pC
of charge on its plates, what is the unknown capacitance?
24. Three concentric, thin conducting cylindrical shells have radii of 0.2, 0.5, and 0.8 cm.
The space between the shells is filled with air. The innermost and outermost cylinders are
connected at one end by a conducting wire. Find the capacitance per unit length of this
system.
25. A rectangular parallel-plate capacitor of length a and width b has a dielectric of width b
partially inserted a distance x between the plates, as shown in Figure . (a) Find the
capacitance as a function of x. Neglect edge effects. (b) Show that your answer gives the
expected results for x = 0 and x = a
26. The two capacitors shown in Figure have capacitances C1 = 0.4 𝜇 and C2 = 1 .2 𝜇F. The
voltages across the two capacitors are V1 and V2, respectively, and the total stored energy
in the two capacitors is 1.14mJ. If terminals band c are connected together, the voltage is

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Va - Vd = 80 V; if terminal a is connected to terminal b, and terminal c is connected to
terminal d, the voltage Va - Vd = 20 V Find the initial voltages V1 and V2
27. Two spheres have radii a and b, and their centers are a distance d apart. Show that the
capacitance of this system is
Provided d is large compared with a and b. Suggestion: Because the spheres are far apart,
assume the potential of each equals the sum of the potentials due to each sphere. (b)
Show that as d approaches infinity, the above result reduces to that of two spherical
capacitors in series
28. Calculate the equivalent capacitance between points a and b in Figure P26.77. Notice that
this system is not a simple series or parallel combination. Suggestion: Assume a potential
difference ∆𝑉 between points a and b. Write expressions for ∆𝑉 in terms of the charges
and capacitances for the various possible pathways from a to b and require conservation
of charge for those capacitor plates that are connected to each other.
29. A parallel-plate capacitor in air has a plate separation of 1.50 cm and a plate area of 25.0
cm2. The plates are charged to a potential difference of 250 V and disconnected from the
source. The capacitor is then immersed in distilled water. Assume the liquid is an
insulator. Determine (a) the charge on the plates before and after immersion, (b) the
capacitance and potential difference after immersion, and (c) the change in energy of the
capacitor.