Electrostatics - Coulomb's Law
March 12-13
Today
• Electrostatic Force/Coulomb's Law
• Examples
• Concept Questions
• HW - online: Electrostatics Problems 2
Period 6
1
Electrostatics - Coulomb's Law
March 12-13
Coulomb's Law: For two charges Q and q, separated by a distance R,
there exists a mutual Electrostatic Force, FE, whose magnitude is
FE = kQq
R2
where k is known as the Electrostatic Constant; in our system of units, the
value of k = 9 E9 Nm2/C2.
The direction of this force depends on the signs of the charges:
• if the charges have the same polarity, the force is REPULSIVE, and FE
will have a "positive" value;
• if the charges have opposite polarity, the force is ATTRACTIVE, and FE
will have a "negative" value.
Period 6
2
Electrostatics - Coulomb's Law
March 12-13
Example 1: Imagine 2 identical +1.0 C charges are placed 1.0 m apart
from each other.
a) How many excess protons would each charge have? Does it seem
reasonable/possible to have that much net charge?
b) What would be the strength of the Electrostatic force between these
charges? Is it attractive, or repulsive?
(To put this force in perspective, a typical car weighs ~2 tons. The force
above would be equivalent to the weight of approximately 1 million cars.)
Period 6
3
Electrostatics - Coulomb's Law
March 12-13
Example 2:
R
The Hydrogen atom is the simplest in structure on the periodic table. In a
hydrogen atom, the nucleus is a single proton (q = 1.6 E-19 C), and it is
orbited by a single electron (Q = -1.6 E-19 C), at an average distance of 5.3
E-11 m. What is the Electrostatic Force between them? What is meant by
the (-) sign?
Example 3:
The mass of a proton is mp = 1.67 E-27 kg, and the mass of the electron is
me = 9.11 E-31 kg. What is the strength of the gravitational force between
them? [FG = Gmpme/R2]
Period 6
4
Electrostatics - Coulomb's Law
March 12-13
Examples 4-8:
Two charges Q and q are separated by a distance R. In this set-up, they
experience a force FE.
4) Without changing the charges, they are moved apart to a distance (3R).
What happens to the Electrostatic Force? [Does it get weaker/stronger/
change direction/no change?] Describe how the "new" force compares to
the original.
5) Without changing the charges, they are moved to a distance (¼R) apart.
What happens to the Electrostatic Force? [Does it get weaker/stronger/
change direction/no change?] Describe how the "new" force compares to
the original.
6) The charges are returned to the same distance R apart. The charge Q is
increased in size to (3Q). What happens to the Electrostatic Force? [Does
it get weaker/stronger/change direction/no change?] Describe how the
"new" force compares to the original.
7) The charges are returned to the same distance R apart. The charge Q is
increased in size to (3Q) and the charge q is increased in size to (3q). What
happens to the Electrostatic Force? [Does it get weaker/stronger/change
direction/no change?] Describe how the "new" force compares to the
original.
8) The charge Q is increased to (3Q) and the charge q is increased to (3q).
The charges are moved apart so that they are separated by a distance (3R).
What happens to the Electrostatic Force? [Does it get weaker/stronger/
change direction/no change?] Describe how the "new" force compares to
the original.
Period 6
5
Electrostatics - Coulomb's Law
March 12-13
"Reasoning" Method:
FE ∝ Q ☜ This implies that, if Q ⇪, then FE ⇪by the same factor; same if
decreasing
FE ∝ (1/R2) ☜ This implies that, if R ⇑, then FE ⇓ by a factor of (R-factor)2;
same if R decreases
"Brute Force" Method:
Period 6
6
Electrostatics - Coulomb's Law
March 12-13
Coulomb's Law: [More than two charges]
In a case where there are more than 2 charges, you can find the "Net"
Electrostatic Force on a single charge by determining the Electrostatic
Force due to each of the other charges, and then adding them as vectors.
I.e., the net FE on charge q1 due to charges q2 and q3 would be equal to
ΣFE1 = FE12 + FE13
*Note: we would have to add these forces as Vectors...
• In a 1D case, consider if the forces are +/• In a 2D case, consider forces in x- and y-directions
Period 6
7
Electrostatics - Coulomb's Law
March 12-13
Example: In the diagram below, q1 = +3 E-10 C, q2 = +4 E-10 C, and q3 =
+3 E-10 C.
2m
q1
1m
q2
q3
What is the ΣFE on q1?
What is the ΣFE on q2?
What is the ΣFE on q3?
Period 6
8