Download Electric Field

Electric Field
ur
ur F
E=
q
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
GMm
F=
2
r
æGM ÷
ö
F = m çç 2 ÷
÷
çè r ø
F
= g
m
q1q2
F = ke 2
r
Qq
F = ke 2
r
F
Q
= ke 2
q
r
F
= E
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?
Solution
• Start with F=ma!
• Free body diagram.
Fe = qE
Fg=mg
• F = qE – mg = 0;
• E=mg/q = 0.0050 x 9.8 / 4.0 x 10-6 =12000 N/C
(12250 if you don’t like sig figs or units)
Drawing!
ur
ur F
E=
q
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
1.0 m
20.0 cm
5.0 cm
Millikan Oil drop experiment
• Shows quantized nature of charge. (He got
the Nobel Prize for this one.)
+
-
Free Body Oil Drop
Drag µ v 2
falling
qE
rising
-q
-q
Drag µ v 2
mg
mg
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 q1q2
F=
2
4pe0 r
You can see that the values of e0 and ke. must be
related.
1
ke =
4pe0
= 8.99 x109 (Nm 2 / C 2 )
e0 = 8.85 x10- 12 (C 2 / Nm 2 )
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
ur
ur F
Q
E=
= ke 2
q
r
Lightning Rods
• What property of charged objects explains
how they work?