Coulomb’s Law
Unit 1
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1 ,2
F
+2
r̂1,2
+1
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
I Like charges: force by 1 on 2 in the
direction r̂1,2
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1 ,2
F
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
I Like charges: force by 1 on 2 in the
+2
direction r̂1,2
I Opposite charges: force by 1 on 2 in
the direction opposite r̂1,2
r̂1,2
+1
~ 1,2
F
r̂1,2
+1
-
2
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1 ,2
F
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
I Like charges: force by 1 on 2 in the
+2
direction r̂1,2
I Opposite charges: force by 1 on 2 in
the direction opposite r̂1,2
r̂1,2
+1
~ 1,2
F
-
2
I In practice: draw a picture!
I Need the components? Set up
coordinates!
r̂1,2
+1
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1 ,2
F
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
I Like charges: force by 1 on 2 in the
+2
direction r̂1,2
I Opposite charges: force by 1 on 2 in
the direction opposite r̂1,2
r̂1,2
+1
~ 1,2
F
-
2
I In practice: draw a picture!
I Need the components? Set up
coordinates!
r̂1,2
+1
I Mathematics: r̂1,2 =
~r2 −~r1
|r~2 −~r1 |
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
~ 1 ,2
F
+2
I ε0 is a constant that has the value
C2
8.85 × 10−12 Nm
2
r̂1,2
+1
~ 1,2
F
r̂1,2
+1
-
2
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
~ 1 ,2
F
+2
I ε0 is a constant that has the value
C2
8.85 × 10−12 Nm
2
r̂1,2
2
+1
~ 1,2
F
r̂1,2
+1
-
2
I The constant K = 8.99 × 109 Nm2
C
Coulomb’s Law: Physics & Math
~ 1,2 = K
F
1 q1 q2
q1 q2
r̂
=
r̂1,2
1
,
2
4πε0 r12,2
r12,2
~ 1,2 = force from 1, on 2
I F
I r̂1,2 = unit vector from 1, to 2
~ 1 ,2
F
+2
I ε0 is a constant that has the value
C2
8.85 × 10−12 Nm
2
r̂1,2
2
+1
~ 1,2
F
r̂1,2
+1
-
2
I The constant K = 8.99 × 109 Nm2
C
I Magnitude:
F1,on 2 =
1 |q1 ||q2 |
2
4πε0 r12
The Principle of Superposition
~ on 1 =
When we have multiple charges: F
P
~ i, on 1
F
Vector algebra is extremely important in this class!
Practice
Consider the two charges ±Q shown below. In which direction is the force that they
exert on the positive charge +q, located midway between the two charges but
displaced upward?
+q
a) Up.
b) Down.
d
c) Left.
d
d) Right.
+Q
d
-Q
e) None of the above
Practice
Consider the two charges ±Q shown below. In which direction is the force that they
exert on the positive charge +q, located midway between the two charges but
displaced upward?
~+
F
~ net
F
+
~−
F
d
a) Up.
b) Down.
c) Left.
d) Right.
d
e) None of the above
+Q
d
-Q
Important concept: symmetry!
Practice
Consider the two charges ±Q shown below. In which direction is the force that they
exert on the positive charge +q, located midway between the two charges but
displaced upward?
~+
F
~ net
F
+
~−
F
d
a) Up.
b) Down.
c) Left.
d) Right.
d
e) None of the above
+Q
d
-Q
Important concept: symmetry!
More Practice
~ 1 | on q1 if it’s sign is changed?
What happens to |F
a) It decreases
b) It increases
c) It stays the same
d) Need to know the sign of q1
More Practice
It stays the same!