TUTORIAL 4A: ELECTROSTATICS
Coulomb’s Law
1. Two charges attract each other with a force of 1.5 N. What will be the force if the
distance between them is reduced to one-ninth of its original value? [120 N]
2. The force of repulsion that two like charges exert on each other is 3.5 N. What will the
force be if the distance between the charges is increased to five times its original value?
[0.14 N]
3. Two spherical objects are separated by a distance of
. The objects are
initially electrically neutral and are very small compared to the distance between them.
Each object acquires the same negative charge due to the addition of electrons. As a
result, each object experiences an electrostatic force that has a magnitude of
. How many electrons did it take to produce the charge on one of the
objects? [8]
4. Two very small spheres are initially neutral and separated by a distance of 0.50 m.
Suppose that 3.0 × 1013 electrons are removed from one sphere and placed on the other.
(a) What is the magnitude of the electrostatic force that acts on each sphere? [0.83 N]
(b) Is the force attractive or repulsive? Why?
5. A charge of 6.00 mC is placed at each corner of a square 1.00 m on a side. Determine the
magnitude and direction of the force on each charge. [6.20 × 105 N away from the
center of the square]
6. Two point charges are located on the y-axis as follows: Charge q1 = - 1.50 nC at
y = - 0.600 m, and charge q2 = +3.20 nC at the origin (y = 0). What is the total force
(magnitude and direction) exerted by these two charges on a third charge q3 = + 5.00 nC
located at y = -0.400 m? [2.58 × 10-6 N, -y direction]
7. Three charges are located at the corners of an equilateral triangle, as shown
below. What is the net electric force (magnitude and direction) acting on the top charge,
q1? Let q1 = +3.50 μC, q2 = +5.00 μC, and q3 = −5.00 μC. [0.630 N in the +x direction]
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Electric Field
8. Four-point charges have the same magnitude of
and are fixed to the corners
of a square that is 4.0 cm on a side. Three of the charges are positive and one is negative.
Determine the magnitude of the net electric field that exists at the center of the square.
[54 N∙C-1]
9. Two charges, –16 and
, are fixed in place and separated by 3.0 m.
(a) At what spot along a line through the charges is the net electric field zero? Locate this
spot relative to the positive charge. (Hint: The spot does not necessarily lie between
the two charges.) [3.0 m]
(b) What would be the force on a charge of
placed at this spot? [0 N]
10. The membrane surrounding a living cell consists of an inner and an outer wall that are
separated by a small space. Assume that the membrane acts like a parallel plate
capacitor in which the effective charge density on the inner and outer walls has a
magnitude of 7.1 × 10-6 C∙m-2.
(a) What is the magnitude of the electric field within the cell membrane?
[8.0 × 105 N∙C-1]
(b) Find the magnitude of the electric force that would be exerted on a potassium ion
(K+; charge = + e) placed inside the membrane. [1.3 × 10-13 N]
11. Two charges are placed on the x axis. One of the charges
is at
x1 = + 3.0 cm and the other
is at x1 = + 9.0 cm. Find the net electric
field (magnitude and direction) at
(a) x = 0 cm [-6.2 × 107 N∙C-1]
(b) x = + 6.0 cm. [+2.9 × 108 N∙C-1]
12. An electric field of 2.6 × 105 N∙C-1 points due west at a certain spot. What are the
magnitude and direction of the force that acts on a charge of
at this spot?
[1.8 N, due east]
PTO
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13. A negative charge (-q) is fixed to one corner of a rectangle, as in the drawing below.
Determine the magnitudes of the positive charges that must be fixed to corner A and to
corner B, so that the total electric field at the remaining corner is zero. Express your
answers in terms of q. HINT: Draw the free-body diagram first. [0.0895 q]
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