1. Coulomb’s Law Like charges repel, and unlike charges attract
The force is proportional to the charges
It depends on distance q1 q2
Other ways of writing this formula
The r-hat just tells you the direction of the force
When working with components, often helps to rewrite the r-hat
Sometimes this formula is written in terms of a quantity0 called the permittivity of free space

2. Now it’s your turn Sample Problem 3.0 mC
Three charges are distributed as shown at right. Where can we place a fourth charge of magnitude 3.0 mC such that the total force on the 1.0 mC vanishes?
3.0 mC  ?
1.0 mC
2.0 mC
1.0 m
1.16 m
2.0 m
Now it’s your turn
-4.0 mC

3. Forces From Continuous Charges
If you have a spread out charge, it is tempting to start by calculating the total charge
Generally not the way to go
The charge of the line is easy to find, Q = L
But the distance and direction is hard to find
To deal with this problem, you have to divide it up into little segments of length dl
Then calculate the charge dQ =  dl for each little piece
Find the separation r for each little piece
Add them up – integrate
For a 2D object, it becomes a double integral
For a 3D object, it becomes a triple integral q r  dl

4. The units for electric field are N/C
The Electric Field
Suppose we have some distribution of charges
We are about to put a small charge q0 at a point r
What will be the force on the charge at r?
Every term in the force is proportional to q0
The answer will be proportional to q0
Call the proportionality constant E, the electric field q0 r
The units for electric field are N/C
It is assumed that the test charge q0 is small enough that the other charges don’t move in response
The electric field E is a function of r, the position
It is a vector field, it has a direction in space everywhere
The electric field is assumed to exist even if there is no test charge q0 present

5. Electric Field From a Point Chargeq q0
From a single point charge, the electric field is easy to find
It points away from positive charges
It points towards negative charges - +

6. Electric Field from Two Charges
Electric field is a vector
We must add the vector components of the contributions of multiple charges + + - +