1. Electric Field

2. Goal of the class To understand electric fields
Question of the day: How does static electricity affect the flow of water and why?

3. Definition of Electric Field
Draw q1 and q2
If we have 2 charges q1 and q2, we know by Coulombs Law that they either attract or repel, based on the charges.
But how do they do this if they’re not touching?
When you want to move a box you have to touch it in order for it to move. This is not the same for electric charges.
The reason is because of this electric field. Force at a distance.
Q1 produces a field around it in a similar way a magnet does. The space around it is different in some way.
When q2 is brought in it’s now sitting in the field produced by q1.
The electric field applies a force to q2 and either pushes or pulls it.
The field is defined in this way. Imagine we have a sphere that is positively charged. (draw a sphere that charged). And we bring in a charge q. It will feel a force F from the field. So if we measure that it sill have a direction.
Now we define the electric field at that point as the force / q = F/q = E
The field is everywhere in space.

4. Field of a Point Charge
Suppose we have a primary point charge q1 and it emits some field.
To find the field we bring a test charge q2 close to it.
Suppose we wish to find E at the distance r away.
We can find the force and divide by q2.
F=kq1q2/r2
E=kq1/r2
The electric field only depends on q1, the source charge.
This is the magnitude, but what’s the direction?
It’s the same direction as the force. So it will be along the radius and out the top.
If we take a positive charge and we can see everywhere the field is radially out. If we draw a sphere the magnitude is the same (as r is the same).
If we have a sphere twice as big, the magnitude is 4 times less (inverse square law) everything is still radial, with same magnitude.
If the charge is negative, the arrows head towards the negative charge.

5. Field of a Collection of Point Charges
Now if we consider a collection of point charge and we want to find the field.
Draw q1 and q2. We want to know the electric field at some point.
The electric field is a vector quantity and we can add them like a vector sum.
The total electric field here is the sum on both electric fields.
If we have an equilateral triangle with Q charge in each corner. There will be a region where the electric field is zero (the middle)

6. Parallel Plate Capacitor
The electric field of a point charge is radial.
As we move away from the point charge the electric field reduces.
Is there a way to create a constant electric field.
It is with a parallel plate capacitor.
If we have 2 plates or area A, and separated by a small distance (comapred to the dimensions of the plate) a small distance d.
Now if we put some positive charge on the top plate and negative on the bottom. +Q and –Q. The electric field starts from the positive and ends of the negative charge. The electric field is down.
E is constant between the plates of a parallel plate capacitor.
How big is the field?
E = Q/e0 A =sigma/A remember e0 = 8.854X10-12 permittivity of free space. Sigma is the surface charge density [C/m2]
Out side the capacitor the electric field is zero.

7. Electric Field Lines
The electric field is a vector and hard to draw so we show field lines to represent it.
Field lines are always tangent to the electric field vector.
So if I draw a positive charge and show the electric field. We connect them tangentially and it shows the field lines.
If we have a positive and negative charge now.
Very close to the positive charge the field lines are radially out and the other is far away. Like an isolated positive charge.
We end up with field lines. We can determine the direction of the electric field at any point now.
What are the rules in drawing the field lines
1: The lines start at positive (source) and go to negative (sink).
2: Lines can never cross.