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1. The force acting between two charged spheres 10 cm apart is 3.0 X 10-6 N. Consider each
of the following changes separately, and determine the resulting force.
a) The distance remains unchanged, but the charges are doubled.
b) One of the spheres is momentarily touched by an identical uncharged sphere.
c) The distance between spheres is changed to 30 cm.
2. A force of 3.6 X 10-5 N exists between two positively charged objects. This repulsive force
is present when the objects are 0.12 m apart. What is the force if the distance between the
charged objects is changed to the following values?
a) 0.24 m b) 0.30 m c) 0.36 m?
3. Three small spheres are fixed at the vertices of an equilateral triangle with sides of length 20 cm.
A charge of 4.0 X 10-6 C is placed on each sphere. Determine the electrical force on each
sphere.
4. The force of attraction between two charged spheres (A and B) is 1.6 X 10-2 N. Each
sphere is touched with an identical neutral sphere. The two spheres (A and B), are then placed
so that they are twice the distance apart as before. Calculate the new force on the spheres.
Assume that the spheres which were originally neutral, are removed after the touch, so that they
will no longer affect the experiment.
5. The traditional model of a hydrogen atom consists of a proton with an electron orbiting around
it in a circular path. The radius of the electron's orbit is 5.3 X 10-11 m. Given that the
masses of a proton and electron are 1.67 X 10-27 kg and 9.11 X 10-31 kg respectively,
answer the following questions.
a) The electrostatic force between the electron and proton is responsible for the orbit of
the electron. What is this force?
b) Calculate the gravitational force between the electron and the proton.
c) Indicate which force (gravitational or electrostatic), is responsible for most of the
electron's centripetal motion.
d) For this orbiting electron, determine the velocity and the period of the motion.
6. Two charged spheres, identical in size, are 30 cm apart. They attract with a force of
8.0 X 10-5 N. The two spheres are touched together and then placed 30 cm apart again.
The new force between them is a repulsive force of 1.0 X 10-5 N.
a) Determine the charges on the two spheres after they touched.
b) Calculate the charge on the two spheres prior to touching.
7. A force of 3.2 N [left] is applied to a charged object with charge of 2.4 X 10-6 C, by creating
an electric field around the charged object. Determine the direction and magnitude of the
electric field.
8. An object (treated as if it were a point in space) has a charge of +5.4 X 10-4 C on it. At a
distance of 3.0 m to the right of the object, what is the electric field?
9. At point Z in the diagram below, an electric field is present due to the charges at X and Y.
What is the direction and magnitude of this field?
10. A pair of oppositely charged parallel plates produce an electric field with magnitude
3.0 X 103 N/C halfway between the plates. What is the electric field intensity halfway
between this midpoint and the positively charged plate?
11. A charged object has an electrical force of 6.0 X 10-6 N [right] applied to it because of the
presence of an electric field. The charge on the object is +1.0 X 10-6 C.
a) At the location of the object, determine the electric field intensity.
b) If this charged object is replaced with an object with a charge of -7.2 X 10-4 C on it,
what force does the new object experience?
12. A positive point charge of 8.0 X 10-3 C produces an electric field around it. What is the
direction and magnitude of this field 1.5 m to the right of the charge?
13. Given the diagram below, determine the direction and magnitude of the electric field at Z.
14. A potential of -6.4 X 104 V exists at a distance of 25 cm from a point charge. Determine the
nature and magnitude of the point charge.
15. An object of charge 1.2 X 10-6 C is moved between points D and E in an electric field. The
amount of work required to make this move is 4.2 X 10-3 J. Determine the potential
difference between D and E.
16. Two charges are 40 cm apart. The magnitude of the charges are 1.0 X 10-6 C and
3.2 X 10-3 C. Calculate the amount of work that was done in moving the smaller charge
from 100 cm away to its present location.
17. What is the energy of an electron which is accelerated from rest through a potential difference
of 2.5 X 104 V?
18. Two protons are brought to within 1.0 X 10-16 m of each other from a very large distance
apart. Calculate the amount of work need to do this.
19. Two parallel plates are 8.0 cm apart. If we want an electric field strength between them of
2.5 X 103 N/C, what potential difference must exist between the plates?
20. Each of two small spheres has a deficit of 1 X 108 electrons. The spheres are 1.0 m apart.
What is the electrical repelling force between them?
21. What is the electric field intensity at a distance of 0.500 m from an object with 5.00 X 109
excess electrons?
22. Two parallel plates are 0.50 cm apart, and have a potential difference between them of 270 V.
Under these conditions, an oil drop is suspended motionless between the two plates. If the
mass of the drop is 2.6 X 10-15 kg, determine the charge and number of excess or deficit
electrons on the oil drop.
23. A parallel plate apparatus has a plate separation of 25 cm. A ping-pong ball of mass 0.10g is
coated with a metallic paint so that a charge of 5.0 X 10-6 C can be placed on the ball. If the
ball is to be suspended motionless between the plates of the parallel plate apparatus, what
potential difference must exist between the plates?
24. A small sphere has 1 X 1012 excess electrons on it. What are the electric potential and
electric field intensity at a point 0.40 m from the sphere?
25. The diagram below shows a ping-pong ball with a mass of 3.0 X 10-4 kg, which is suspended
by a thread of length 1.0 m. The two vertical plates have a distance of 10 cm between them.
The ball is forced to the side a distance of 1.0 cm, when an electric potential of 420 V exists
between the two vertical plates.
a) Calculate the electric field intensity between the plates.
b) Determine how much tension is in the thread.
c) What electric force is applied to the ball by the electric field between the plates?
d) Calculate the charge on the ping-pong ball.
26. When moving a small charge from one electrical plate to another, the work done is 0.24 J.
The potential difference between the parallel plates is 1.5 X 102 V. What is the magnitude
of the charge?
27. The charge on an alpha particle is +2e, while the mass is 6.6 X 10-27 kg. The alpha particle
is placed between the plates of a parallel plates apparatus, which has a potential difference of
2.0 X 103 V between the plates. Assuming the alpha particle starts from rest, determine its
velocity when it reaches the negative plate of the apparatus if
a) it starts near the positive plate.
b) it starts at the midpoint between the plates.
28. Assuming it is possible to release two electrons from rest when they are 1.0 X 10-12 m apart,
calculate the kinetic energy and speed of each when they are a "large" distance apart.
29. A parallel plate apparatus has a potential difference of 500 V between the plates. An
electron is released near the negative plate of the apparatus. The experiment is performed in
a vacuum, and the electron's initial speed is 0.0 m/s. What is the electron's speed when it
collides with the positive plate?
30. After passing through a small hole in the positive plate of a parallel plate apparatus, an
electron moves across a vacuum and strikes the negative plate with a velocity of
1.0 X 106 m/s. The electron was moving at 5.0 X 106 m/s when it went through the hole.
Determine the potential difference between the plates.
31. The mass of an alpha particle is 6.6 X 10-27 kg, while its charge is 3.2 X 10-19 C. Two
alpha particles travel towards each other along a "head-on collision" path. They both are
initially moving with a speed of 3.0 X 106 m/s. What is the minimum separation between the
alpha particles?
December 30, 2013
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