**Electrostatics**

The electric field

2.1.1 Introduce electrostatics

2.1.2 Coulomb's Law

2.1.3 The Electric Field

2.1.4 Continuous Charge Distributions

**Electrostatics**

Main principles

Electrostatics = Source charges are stationary

Charges exert forces on other charges

Superposition for multiple charges

Moving charges more complicated

**Coulomb's Law**

Force on a test charge Q from a stationary charge q a distance of r away.

tricky bits

R hat. This is a vector and it points either towards or away from the source charge.

R. It is the vector that points from the source charge to the test charge.

Quiz!

**The Electric Field**

From the principle of Superposition, there is only one E field.

Note is a function of position r. (buried in the r hat)

What is it? Think of it as a field.

Continuous distribution of charge

Tricky bits

dq: either line, surface or volume charge densities.

R hat: has the vector direction part. Needs to be in the units of integration.

R : is the length of the vector pointing from each little source charge element to point of interest.

2

**Continuous Distributions**

These change the integral

Note:

Depend upon the integration variable

And it can be variable

Line Charge

p

r

E

r` = x

x

z

0

Consider a line of charge, 2L, on x axis, what is the E field at pt. Z above the midpt.

Find

dq

symmetry, Z direction only, needs

R

R hat

Line Charge

p

r

E

r` = x

x

z

0

Collect

**Binomial expansion**

What happens when z>>L or L>>z ?

for 1>>x

for z>>L

**how about L>>z**

1 of the 5 charges has been removed, as show. What's the E field at the center?

a) +(kq/a ) j

b) -(kq/a ) j

c) 0

d) Something entirely different!

e) This is a nasty problem

**Practice**

**Gut feeling ?!?**

**Prove it!**

**Do you dare find this?**

(not in this coordinate system)

"Can you go over different charge distribution integrals with us (line, surface, and volume)?

"I don't think that I fully understand why they split the problem up in example 2.1"

**Ring charge**

"why is electric force not an action at a distance force"

E field

What is the E field from a ring of charge with uniform charge density lambda, having radius a and at position z?

Disk Charge?

z

a

find:

dq

R

Rhat