MOUNT ROYAL UNIVERSITY
DEPARTMENT OF CHEMISTRY AND PHYSICS
CLASSICAL PHYSICS II (PHYS 1202)
Assignment #3 (20 points)
Name: ________________________________________
Professor: Manuel Diaz-Avila
Due Date: Thursday, March 10, 2022
Problem 1 (2 points): A 15-μF air-filled capacitor is connected to a 50-V voltage source and becomes fully charged.
The voltage source is then removed and a slab of dielectric that completely fills the space between the plates is
inserted. The dielectric has a dielectric constant of 5.0.
a) What is the capacitance of the capacitor after the slab has been inserted? (1)
b) What is the potential difference across the plates of the capacitor after the slab has been inserted? (1)
Problem 2 (5 points):A 1.0 μF capacitor has a potential difference of 6.0 V applied across its plates. If the potential
difference across its plates is increased to 8.0 V, how much additional energy does the capacitor store?
Problem 3 (5 points): The membrane that surrounds a certain type of living cell has a surface area of 5.0x10-9 m2 and
a thickness of 1.0 x10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric
constant κ=5.0. The potential difference between the inner surface of the membrane and the outer surface is +60mV,
i.e. outer surface is at higher potential.
a) Calculate the capacitance of the membrane. (1)
b) How much charge resides on the outer surface of the membrane? (1)
c) Calculate the magnitude of the electric field inside the membrane. (1)
d) Calculate the work required to move a potassium ion (charge +1.60x10-19 C) from the inner surface of the
membrane to the outer surface of the membrane. (1)
e) Calculate the energy stored in the membrane. (1)
Problem 4 (5 points): A spherical capacitor has an inner radius of 8.00 mm and an outer radius of 8.50 mm. With air
between the spheres, the capacitor is connected to a battery and allowed to charge fully. With the battery still
connected, oil is poured in, filling the volume between the spheres. As the oil is added, the battery does an additional
8.90 nJ of work on the capacitor. Determine the electric potential difference (voltage0 supplied by the battery.
Problem 5 (3 points): The long thin cylindrical axon of a nerve carries nerve impulses. The axon can be as long as 1 m
and the capacitance is given by:
C=
2πκε o L
ln
( )
R2
R1
a) Calculate the capacitance of a 1.0 m long axon of radius 4.5×10−6 m with a membrane thickness of 7.1×10−9 m. The
dielectric constant of the membrane material is about 7.0. (1)
b) Determine the magnitude of the charge on the inside (negative) and outside (positive) of the membrane wall if
there is a 0.076 V potential difference across the wall. (1)
c) Determine the energy stored in this axon capacitor when charged. (1)