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KIGALI INSTITUTE OF SCIENCE AND TECHNOLOGY
INSTITUT DES SCIENCES ET TECHNOLOGIE
Avenue de l'Armée, B.P. 3900 Kigali, Rwanda
INSTITUTE EXAMINATIONS – ACADEMIC YEAR 2012-13
MAIN EXAMINATION
FACULTY OF SCIENCE
PHYSICS and MATHS
YEAR I SEMESTER II
PHY3121 ELECTRICITY AND MAGNETISM I
DATE:
TIME: 2 HOURS
MAXIMUM MARKS = 60
INSTRUCTIONS
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This paper contains FOUR (4) questions divided in two sections ( A and B)
Answer the whole first question in section A.
Answer any Two questions in section B
The first question counts 30 marks.
Each question count 15 marks in section B
No written materials allowed.
Write all answers in the booklet provided.
Do not forget to write your Registration Number.
Do not write any answers on this question paper.
SECTION A
QUESTION 1 (30 MARKS)
a. Using Gauss’s law, determine the electric field due to a uniform spherical charge
distribution, of radius “R” at a distance r from the centre of the charge distribution,
when r < R. (5marks)
b. A particle of charge q1  6.0C is located on the x-axis at the point x1  5.1cm . A
second particle of charge q 2  5.0C is placed on the x-axis at x2  3.4cm . What is the
magnitude and direction of the total electrostatic force acting on a third particle of charge
q3  2C placed at the origin (x = 0)? (5marks)
c. Two charged metal plates in vacuum are 15cm apart. The electric field between the plates
is uniform and has a strength of E=3000N/C. An electron ( q  e , me  9.31 10 31 kg)
is released from rest at point P just outside the negative plate (i) How long will it take to
reach the other plate? (ii) How fast will it be going just before it hits? (5marks)
d. i) Due to a uniform electric field, 0.01mJ energy is stored in region of volume of 100 cm 3
in vacuum. What is the magnitude of the electric field in the region?(3marks)
ii) Explain why electric field is zero inside the conductor? (3marks)
e. Write the loop rule for loops abcda and befcb, and the junction rule at b in the network
shown in the figure below. Assume the currents as shown in the figure below (4marks)
f) Convert the integral form of Ampere’s law for magnetic field in to a differential form.
(5marks)
SECTION B (30 MARKS)
QUESTION 2 (15MARKS)
a. Using Gauss’s law, determine the electric field at a point due to the charge, which is
uniformly distributed on one side of a non-conducting infinite sheet. The surface charge
density on the sheet is  . (10marks)
b. An air filled parallel plate capacitor has a capacitance of 5.0 pF . A potential of 100 V is
applied across the plates, which are 1.0cm apart, using a storage battery. What is the
energy stored in the capacitor? Suppose that the battery is disconnected, and the plates
are moved until they are 2.0cm apart. What now is the energy stored in the capacitor?
Suppose, instead, that the battery is left connected, and the plates are again moved until
they are 2.0cm apart. What is the energy stored in the capacitor in this case? (5marks)
QUESTION 3 (15MARKS)
a. Write Ampere’s law for magnetic field in integral form and interpret it (5 marks)
b. Determine the magnetic field outside a long straight wire with current I, at a distance r
from the axis of the wire. (10marks)
QUESTION 4 (15 MARKS)
Find the three currents I1, I2 and I3 in the circuit shown in the diagram
Where R1 = 100Ω, R2 = 10Ω, R3 = 5Ω, 1  12V and  2  6V .
Good luck