Electric Potential
Studio Physics I
In this activity, we will ignore relativistic and quantum mechanical effects. If you
don’t know what those are, don’t worry, we are ignoring them! (If you want a tiny
taste of the theory of relativity, and you have the time, see question 9.)
Use the following constants:
M = mass of a proton = 1.67 × 10–27 kg
m = mass of an electron = 9.1 × 10–31 kg
1 e = 1.6 × 10–19 C
Part I – Electric Potential, Potential Energy, and Kinetic Energy
1. Explain in a few complete sentences the difference between electric potential and
electric potential energy. What is the relationship of one to the other?
2. Consider the configuration shown below. Let the electric potential be defined as zero
at infinity. What is the electric potential, with correct units, at points A, B, C, and D?
(“X” marks the spot for each of the points.)
D
B
C
1 cm
-1 C
A
+1 C
6
1 C  1  10 C
(All lengths are 1 cm and all angles at intersections are 90º.)
3. Is the electric field zero at the points where the electric potential is zero? If yes,
explain why. If not, explain how it is possible for the electric potential to be zero at a
point where the electric field is not zero.
4. An electron begins at “infinity” (very far away) with K.E. = 3.2 × 10–14 J. What is the
K.E. of the electron at points A, B, C, and D? What is the speed of the electron at D?
(You should get a value greater than c, the speed of light. See question 9.)
5. A proton begins at “infinity” (very far away) with K.E. = 3.2 × 10–14 J. What is the
K.E. of the proton at points A, B, and D? What is the speed of the proton at D? Can
the proton reach point C? If so, what is its K.E. at C? If not, why not?
Rev. 2003 Bedrosian
6. An alpha particle is the nucleus of a He atom, with two neutrons and two protons. An
alpha particle begins at “infinity” (very far away) with K.E. = 3.2 × 10–14 J. Can the
alpha particle reach point D? If so, what is its K.E. at D? If not, why not?
Part II – Electric Potential and Electric Field
7. Copy the figure below to your paper. This figure shows equipotental lines and values
of potentials. Draw the electric field lines, with arrows indicating direction, and find
the X and Y components of the electric field.
Y
X
V=0
X = 0 cm
V = 50
X = 2 cm
V = 100
X = 4 cm
8. Copy the figure below to your paper. This figure shows electric field lines. The
electric field is constant and is equal to 1,000 N/C in the +Y direction. Draw four or
five equipotential lines and label them with locations and values. (Hint: The V = 0
line is your choice, as are the scale and distance between equipotential lines.)
Y
X
Part III – Relativity if You Have The Time
9. There is nothing to prevent a particle from gaining so much kinetic energy that our
Physics I formulas would predict a speed greater than c = 3.0 × 108 m/s, the speed of
light. In order to do the calculation correctly, we need to use Einstein’s Special
Theory of Relativity. According to Einstein, the total energy of a particle is
c
K 2  2 K m c 2 . (K is K.E.) Show
E  K  m c 2 and the speed is given by v 
E
that the speed of the electron in question 4 is 2.4 × 108 m/s using the formula above.
2K
Show that this formula reduces to v 
when K is much smaller than m c2.
m
Rev. 2003 Bedrosian