Download Chapter One: Introduction

Chapter Sixteen:
Problems
Note: These problems come from "Fundamentals of Senior Physics" by Parham and Webber.
1.
(a)
(b)
Two like charges experience a force F upon each other when placed a fixed distance
apart in air. What is the magnitude of the force if the distance between the two charges
is:
doubled
halved?
What is the magnitude of the force if the magnitude of one of the charges is:
(a)
doubled
(b)
halved?
2.
(a)
(b)
(c)
3.
How much must you alter the distance between two charged objects in order to keep the
force between them constant, if you also:
treble the net charge on each
halve the net charge on each
double the charge on one and halve the charge on the other?
A positive test charge is placed 1/3 of the distance between two equally charged positive
objects. The force on the test charge exerted by the near object is F. Determine the force
exerted by the the further object on the test charge, and hence the resultant force on the
test charge.
What is the new resultant force if the charge on the further object is:
(a)
made 3 times as great
(b)
made 3 times as great and negative?
4. You are supplied with the formula:
F = k
q 1q
d2
2
where k has a value of 9×109 Nm2C-2 in a vacuum.
(a) What does each symbol in the formula represent, and what is the situation that the formula
describes?
(b) What is the force between a positive charge of 5 microcoulombs and a negative charge of 8
microcoulombs separated in air by a distance of 0.4m?
(c)
Two equal positive charges experience a force of repulsion of 3.6N when placed
30cm apart in air. What is the value of each charge?
5. How far apart in air must two charges be placed, each having a net charge of 2 coulombs, so
that the force between them is 1 newton?
6. Two equal, small conducting spheres carrying charges of +1.0×10-7C and –2.4×10-7C are
touched together and then placed 3.5cm apart in air. With what force do they act on each
other? Is the force one of attraction or repulsion?
7. Four identical conducting spheres, A, B, C and D are suspended by silk threads. Ball A is
touched by a charged rod and then each of the other three is brought into contact with A and
removed, one at a time. When A and B are placed with their centres 5cm apart, they repel
each other with a force of 1.6×10-6N. How much charges was initially given to A?
8. The electron in a hydrogen atom can be considered to be approximately 5.0×10-11m away
from the proton nucleus. What is the force of attraction between the proton and the
electron?
9. Find the strength and direction of the electric field at a point 10cm due north of a small shere
carrying a charge of 3×10-6C. What would be the force on an electron placed at that
point?
10. Copy the sketches shown below and then complete each sketch by drawing in electric lines
of force. Use an arrow to show which way an electron would move if placed at P.
+
-
+
+
+
+
11. An uncharged metal sphere is suspended between two plates as shown below. Which of the
fields sketched is a correct representation of the resultant field?
A
B
-
+
-
+
D
C
-
+
-
+
E
-
+
12. Below is a representation of the electric field between two metal places.
P
+
-
(a)
What features of the lines of force indicate that the field between the metal places is
uniform?
(b)
Which of the graphs below could represent the force on a positive charge as it moves
from point P towards plate A? Explain your answer.
B
force
force
A
d ista nc e fro m P
d ista nc e fro m P
force
C
d ista nc e fro m P
13. A positive charge of 5×10-5C experiences a force of 0.3N in an electric field. What is the
electric field strength at that point?
14. An electron with charge 1.6×10-19 coulomb is placed in a uniform electric field of strength
100 newtons per coulomb.
(a)
Calculate the force on the electron.
(b)
What would be the force on a proton placed in the same field? Explain the differences in
the consequent motion of the electron and the proton.
(c)
The mass of the electron is 9.1×10-31kg. Calculate its acceleration in the electric field.
(d)
What would be the acceleration of an electron in a gravitational field of 9.8N.kg-1?
15. Check the equation used to evaluate at any point the electric field strength due to a point
charge q and then calculated the electric field strength at a point 6cm away from a
positive point charges of 8×10-6 coulomb.
16. The electric field strength at a point 4.0cm from an isolated point charge is 6.0NC-1. What is
the electric field strength at a point 2.0cm from the charge?
17. Two small charged spheres carrying charges of +1.0×10-8C and +4.0×10-8C respectively are
placed 6cm apart. Find the location of the point between them at which the electric field
strength is zero.
18. Two point charges are placed 10cm apart in air as shown below. One is a positive charge of
8×10-6 coulomb, the other a negative charge of 1.6×10-5 coulomb. Calculate the
resultant electric field strength at the points:
(a)
M which is midway between the two charges, and
(b)
P which is 6cm from the positive charge and 8cm from the negative charge.
19. Determine the resultant electric field strength at the centre of an equilateral triangle if three
point charges of the same magnitude and sign are situated at the vertices. What would
be the field strength if one of the charges were opposite in sign to the others?
20. Charged latex spheres which would normally fall under the action of gravity are held
stationary in the electric field between two charged plates. The electric field is adjusted
until the electric force on a sphere just balances the force downwards due to the
gravitational field. If a sphere of mass 2.4×10-12kg is held stationary by an electric field
of 4.9×104 newtons per coulomb, calculate the charge on the latex sphere. How many
excess electrons are there on the sphere?
21. An alpha particle is a He nucleus; it has a mass of 6.68×10-27kg and a net positive charge of
2×1.6×10-19C. What strength and direction of electric field is required to support its
weight at the surface of the earth?