MULUNGUSHI UNIVERSITY
PHY – 102
Tutorial Sheet 5
1. A 35 𝜇𝐶 point charge is placed 32 𝑐𝑚 from an identical 32 𝜇𝐶 charge. How much work would
be required to move a 0.50 𝜇𝐶 charge from a point midway between them to a point 12 𝑐𝑚 closer
to either of the charges?
2. Three charges are at the vertices of an isosceles triangle. With 𝑞=7.00 𝑛𝐶, the two charges at the base of
the triangle are separated by 2.00 𝑐𝑚 and each have a charge of −𝑞. The charge q at the top of the triangle
is 4.00 𝑐𝑚 from each of the charges at the base. Calculate the electric potential halfway between the charges
on the base of the triangle.
3. (a) Show that the capacitance of a parallel-plate capacitor is given by the equation
(b) A 1-megabit computer memory chip contains many 60.0×10−15 𝐹 capacitors. Each capacitor
has a plate area of 21.0×10−12 𝑚2. Determine the plate separation of such a capacitor. (Assume a
parallel-plate configuration.) The diameter of atom is on the order of 10−10 𝑚 = 1 ˚ 𝐴. Express the
plate separation in angstroms.
4. A PHY-102 student at Mulungushi University wants to make a simple 10 𝑛𝐹 capacitor for tuning
her crystal radio, using two sheets of aluminum foil as plates, with a few sheets of paper between
them as a dielectric. The paper has a dielectric constant of 3.0, and the thickness of one sheet of it
is 0.20 mm. If the sheets of paper measure 22×28 𝑐𝑚 and she cuts the aluminum foil to the same
dimensions, how many sheets of paper would she use between her plates to get the proper
capacitance?
5. Find the equivalent capacitance of the group of capacitors shown in the figure below.
6. Four capacitors are connected as shown below, where 𝐶1= 15.0 μ𝐹, 𝐶2=3.00 μ𝐹, 𝐶3=6.00 μ𝐹,
and 𝐶4=20.0 μ𝐹. (a) Find the equivalent capacitance between points a and b. (b) Calculate the
charge on each capacitor if a 15.0 𝑉 battery is connected across points 𝑎 and 𝑏.
7. A sphere of radius 𝑎 has a charge +𝑞 uniformly distributed throughout its volume. The sphere
is concentric with a spherical shell of inner radius 𝑏 and outer radius 𝑐, as shown in the diagram.
The shell has a net charge of −𝑞. (a) What are the net charged on the inner and outer surfaces of
the shell? (b) Find the expression for the electric field, as a function of radius 𝑟, (i) within the
sphere, (ii) between the sphere and the shell (𝑎<𝑟<𝑏), (iii) inside the shell (𝑏<𝑟<𝑐), (iv) outside the
shell (𝑟>𝑐). (c) Find an expression for the capacitance of the system.
8. Two identical charges 𝑞=2.0 𝜇𝐶 are fixed in space at a distance 𝑑=2.0 𝑐𝑚 apart (see figure). (i)
Find the electric potential at point c. (ii) You bring a third charge 𝑞=2.0 𝜇𝐶 very slowly from
infinity to c. How much work must you do? (iii) What is the potential energy of the configuration
when the third charge is in place?