Instructor: Chilukusha DC
MULUNGUSHI UNIVERSITY
PHY 231 – ELECTRIC AND MAGNETIC FIELDS
2020/2021 ACADEMIC YEAR
TEST ONE (1)
Instructions:
1. Full-time students: Attempt any Three (3) questions.
2. ODL students: Attempt Question 1 (compulsory) and any Other Two (2) questions.
3. Duration:
Full-time students: 1 hour 30 mins
ODL students: 2 hours
1. (a) Distinguish between discrete and continuous charge distribution.
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(b) If an object made of substance A rubs an object made of substance B, then A becomes
positively charged and B becomes negatively charged. If, however, an object made of
substance A is rubbed against an object made of substance C, then A becomes negatively
charged. What will happen if an object made of substance B is rubbed against an object
made of of substance C? Explain your response.
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(c) Two equal and opposite point charges (|𝑞| = 12 𝜇𝐶) are held at a fixed distance 2a apart,
where 𝑎 = 15 𝑐𝑚. Consider plane that is normal to the line joining these two charges and
mid-way between them.
(d) (i) Find the radius R of the circle in this plane for which the electric field is maximum.
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(ii) Calculate the Coulomb force exerted on a point charge 𝑞 = 10 𝜇𝐶 placed at that point.
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2. (a)(i) Explain what is meant by the statement that electrostatic forces obey the principle of linear
superposition.
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(ii) In the figure below, find the resultant force on the +2q charge. Assume 𝑞 = 1.13 𝜇𝐶 and
the side length of the square is 15.2 𝑐𝑚.
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Instructor: Chilukusha DC
(b) A rod of length l has a uniform positive charge per unit length λ and a total charge Q.
Calculate the electric field at a point P that is located along the long axis of the rod and d
distance a from one end.
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3. (a) Distinguish between the structure of conductors and insulators at atomic level.
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(b) (i) Show that the Electric field intensity at a point on the axis of a uniformly charged ring
of radius R, a distance x from its center, is given by
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1
𝑄𝑥
𝐸=
̂
3 𝑥
4𝜋𝜀0 2
2
(𝑅 + 𝑥 )2
(ii) Check the above expression in the limiting case x≫R. Does it yield the expected
results?
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(c) Consider now a uniformly charged right circular cylindrical shell having total charge 𝑄,
radius 𝑅, and height ℎ. Determine the electric field at a point a distance d from the right
side of the cylinder. (Hint: treat the cylinder as a collection of ring charges.)
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4. (a) Capacitors are often stored with a wire connected across their terminals. Why is this done?
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(b) (i) Use Gauss Flux theorem to show that the electric field due to an infinite sheet of charge
is given by
𝐸=
𝜎
2𝜀0
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(ii) Hence or otherwise, show that the capacitance of a parallel-plate capacitor is
𝐶=
𝜀0 𝐴
𝑑
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(c) Two equal but opposite charges +q and –q are separated by a distance of 10 cm in air. What
value of 𝑞 will provide for an electric field strength midway between charges that will
exceed the dielectric strength of air?
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(d) Show that the energy density of a parallel plate capacitor is
1
𝑢 = 𝜀0 𝐸 2
2
END OF TEST
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