Electric Field

FE

q=

urur

Objectives

1. Properly explain/predict the behavior of objects, before and after being electrically charged/discharged.

2. Use equations and constants to solve word problems involving electric field, forces and motions of charged particles.

Definition• Electric Field is defined as Force per charge• Units are Newtons per Coulomb (N/C)• So, what’s an “Electric Field?”• You have probably heard or even spoken of a “FORCE FIELD”

– Esp in science fiction• You have been using equations to describe Gravity Fields already.

• Let’s see how such “Force Fields” compare.

Gravity vs. Electricity

2

2

GMmF

rGM

F mr

Fg

m

=

æ ö÷ç= ÷ç ÷çè ø

=

1 22

2

2

e

e

e

q qF k

rQq

F kr

F Qk

q r

FE

q

=

=

=

=

Gravity Field Electric Field

Note

• Little q, the “test” charge needs to be very small so that its own field will not significantly change the charge distribution causing the surrounding field.

• Charge on a small object can be treated as if it is concentrated at a point, we call this a “point charge.”

Example 1

• A metal covered Styrofoam ball of mass 0.0050 kg and charged to 4.0 micro C is placed in an electric field and suspended motionless in midair. What is the strength of the electric field?

• Start with F=ma!• Free body diagram.

• F = qE – mg = 0;• E=mg/q = 0.0050 x 9.8 / 4.0 x 10-6 =12000 N/C

Solution

Fg=mg

Fe = qE

(12250 if you don’t like sig figs or units)

Drawing! FE

q=

urur

Forces are vectors, so too must be the Electric Field. There are some conventions for drawing lines to represent an electric field, that will help explain the behavior of charged objects.

Sign - Arrows on field lines point away from positive charge. They show the direction of force by the field on a positively charged particle.

Density – The number of lines leaving/ending at an object are drawn in proportion to their charge. They represent the relative strength of the field.

Example 2

• Point charge

+q

Example 3

• Electric dipole• Equal number of lines originate

from pos charge and terminate at neg charge.

• Note symmetry.

http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/dipole.html

Conductors and Insulators

• Conductors – charge (electrons) moves freely – (metals)

• Insulators, …they don’t! (rubber, plastic, glass)

• Field lines can help us determine where the charge on a conductor will reside.

• Four rules…

Rules for electrostatic equilibrium

1. Electric Field is zero everywhere INSIDE a conducting material.

2. Excess charge on a conductor resides entirely on its surface.

3. The electric field caused by a charged conductor is always perpendicular to its surface.

4. Charge is more concentrated at the smaller radius of irregularly shaped objects.

Why?

1. If there were an electric field inside a conductor, what would happen to the charge there?

2. It’s complicated, but has to do with inverse square nature Coulomb’s Law.

3. If it weren’t perpendicular, it would shove the charges sideways, not equilibrium.

4. Less sideways component of force.

Van De Graaff

• A number of the properties we’ve discussed can be demonstrated.

• Like charges repel

• Net Charge migrates to the outside

• Field Lines perpendicular

• “Dipole”

How it works!

One more note on the “point charge”.

• So the charge on the dome of a Van de Graaff is on the dome surface.

• Through methods of calculus you could show that the field created can be determined if you consider all the charge to be located all at the center. This is due to symmetry and charge repulsion.

• You can also show that the field everywhere inside is zero.• This will greatly simplify calculations you will need to do.

Example 4

• A Van de Graaff dome of radius 0.20 meters is charged to 3.00 x 10-4 C. What is the strength and direction of the electric field at the following distances from the center?– 5.0 cm– 20.0 cm– 1.0 meter

Picture

5.0 cm

20.0 cm

1.0 m

Millikan Oil drop experiment

• Shows quantized nature of charge. (He got the Nobel Prize for this one.)

+

-

Free Body Oil Drop

-q

qE

mg

2Drag vµ

rising

-q

mg

2Drag vµfalling

http://chemistry.umeche.maine.edu/~amar/fall2004/Millikan.html

Faraday Ice Pail Experiment

• Charge will migrate outward in conductors.

• Touch a charged conductor to another just like it, ½ the charge will move to it.

• But if you touch the inside of the neutral container, all of it will transfer!

• Let’s draw to explain.

Note

• Coulomb’s Law is also written as: 1 2

20

1

4

q qF

rpe=

You can see that the values of 0 and ke. must be related.

( )

( )

9 2 2

0

12 2 20

18.99 10 /

4

8.85 10 /

ek x Nm C

x C Nm

pe

e -

= =

=

Wrap up

1. Properly explain/predict the behavior of objects, before and after being electrically charged/discharged.

2. Use equations and constants to solve word problems involving electric field, forces and motions of charged particles.

Summary• Like charges repel, opposites attract

• Charge is conserved, stripping one electron leaves a net charge of +e one beind and -e with the electron.

• Net charge resides on surface

• Concentrates at small radius

• No field inside

• Field lines perpendicular

• Point in direction a positive charge will be accelerated.

• Charge is quantized at 1.6 x 10-19 C per elementary charge.

• Charge from one object will be shared with a neutral object if touched on the outside• Charge will be completly given away when charged object is touched inside another

Electric Field

2e

F QE k

q r= =

urur

Lightning Rods

• What property of charged objects explains how they work?