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

2. Electric Field Lines + -
Electric field lines are a good way to visualize how electric fields work
They are continuous oriented lines showing the direction of the electric field + -
They never cross
Where they are close together, the field is strong
The bigger the charge, the more field lines come out
They start on positive charges and end on negative charges (or infinity)

3. Sketch the field lines coming from the charges below, if q is positive
Sample Problem
Sketch the field lines coming from the charges below, if q is positive
Let’s have four lines for each unit of q
Eight lines coming from red, eight going into green, four coming from blue
Most of the “source” lines from red and blue will “sink” into green
Remaining lines must go to infinity
+2q
-2q +q

4. Acceleration in a Constant Electric Field
If a charged particle is in a constant electric field, it is easy to figure out what happens
We can then use all standard formulas for constant acceleration
A proton accelerates from rest in a constant electric field of 100 N/C. How far must it accelerate to reach escape velocity from the Earth ( km/s)?
Look up the mass and charge of a proton
Find the acceleration
Use PHY 113 formulas to get the distance
Solve for the distance

5. Gauss’s Law Electric Flux
Electric flux is the amount of electric field going across a surface
It is defined in terms of a direction, or normal unit vector, perpendicular to the surface
For a constant electric field, and a flat surface, it is easy to calculate
Denoted by E
Units of Nm2/C
When the surface is flat, and the fields are constant, you can just use multiplication to get the flux
When the surface is curved, or the fields are not constant, you have to perform an integration

6. Electric Flux For a Cylinder
A point charge q is at the center of a cylinder of radius a and height 2b. What is the electric flux out of (a) each end and (b) the lateral surface? 
top s b b  r r z
Consider a ring of radius s and thickness ds a q b a
lateral surface