Electricity and Magenetism (PHYS2239)
BSc, Physics - PHYS
Semester: Second Semester
Level: 200
Year: 2017
THE UNIVERSITY OF BAMENDA
FACULTY OF SCIENCE PHYSICS DEPARTMENT
CONTINUOUS ASSESSMENT
COURSE: PHYS3225 - PRINCIPLES OF ELECTRICITY AND MAGNETISM
DATE: Saturday, 8
th
July 2017 DURATION: 2 hours
Permittivity of free space
0
= 8.85 x 10
-12
F/m; permeability of free space
0
= 4 X 10
-7
N/A
2
;
Elementary charge e =1.60 x 10
-19
C; mass of electron m
e
= 9.101 X 10
-31
kg; coulomb constant
k=
= 8.99 x 10
9
Nm
2
/C
2
'
1) a) State two properties of electrostatic field lines.
b) Sketch the electric field lines for an electric dipole.
c) The electric potential at a point is given by V (x, y) = x
2
+ x — 3xy
2
— y
5
+ 7. Calculate the electric field
at that point.
d) A capacitor is connected to a battery. What happens to the energy when a dielectric plate is inserted? Explain
your answer. (8 marks)
2) Shown in figure 1 is the cross-section of a conducting sphere of radius-, surrounded by a very thin conducting
spherical shell of radius R. The inner sphere carries a charge +Q
0
uniformly distributed with a charge density and
the outer shell carries a charge - Q
0
.
a) On the figure, indicate the distribution of charge on the inner sphere.
b) Express p as function of R.
c) Using Gauss's Law, find the strength of the electric field E(r) at given a point, as a
function of r, where r is the distance of the point from the center of the sphere:
i) for r <
ii) for r > R
(7 marks)
3) Figure 2 is a circuit with four branches. The currents I
a
and I
2
, and the emf
ε
1
are unknown. The current flowing
from c to e is 2A.
a) What is the current flowing through each of the 12Ω resistors?
b) What is the value of the emf
ε
1
?
c) What are the currents I
2
and I
2
and in what directions do they flow?
d) Is the emf
ε
2
providing energy or is it absorbing energy? What is the
power it is providing or absorbing? (7 marks)
4) Consider eight of the ions of Cl
-
and Na
+
on a crystal lattice of common salt as shown in figure 3. The ions
are located at the vertices of a cube of side measuring 2.82x10
-10
m as shown in
figure 3. Calculate the magnitude of the electric force that seven of these ions exert
on the eighth.
(8 marks)
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