Transcript 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
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)
ur
ur F
E=
q
Forces are vectors, so too must be the Electric Field.
Sign - Arrows on field lines point away from positive
charge. They show the direction of force by the field on a
positively charged particle.
Drawing!
• Point charge
+q
Dipole
• Electric dipole
• Equal number of lines originate
from pos charge and terminate
at neg charge.
• Note symmetry.
Example 2
r
q, m
Q
What is the acceleration of the small sphere?
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.
Rules for electrostatic
equilibrium
Rule #1: Electric Field is zero everywhere INSIDE a
conducting material.
Reasoning: If there were an electric field inside a
conductor, what would happen to the charge
there?
Rules for electrostatic
equilibrium
Rule #2: Excess charge on a conductor resides
entirely on its surface.
Reasoning: It’s complicated, but has to do with
inverse square nature Coulomb’s Law.
Think back to rule #1
Rules for electrostatic
equilibrium
Rule #3. The electric field caused by a charged
conductor is always perpendicular to its surface.
Reasoning: If it weren’t perpendicular, it would
shove the charges sideways, not equilibrium.
Rules for electrostatic
equilibrium
Rule #4. Charge is more concentrated at the smaller
radius of irregularly shaped objects.
Reasoning: 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!
Example 3
• 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
Electric Field
ur
ur F
Q
E=
= ke 2
q
r
For point charges
The electric field may also be uniform, or approximated that
way in many cases. This will simplify your math, just like
little “g” simplifies things near the Earth’s surface.
uur
ur
Fe = qE
W = mg
Millikan Oil drop experiment
• Shows quantized nature of charge. (He got
the Nobel Prize for this one.)
+
-
Free Body Oil Drop
Drag µ v
falling
qE
rising
-q
-q
Drag µ v
mg
mg
http://chemistry.umeche.maine.edu/~amar/fall2004/Millikan.html
Example 4
q
m
E
What is the charge, Q, on the sphere?
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.
AP note
• Your equation sheet
shows Coulomb’s Law
as:
1 q1q2
F=
2
4pe0 r
It also shows the value of e0 and ke. You can see they
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 to surface
•
Point in direction a positive charge will be accelerated.
•
Charge is quantized at 1.6 x 10-19 C per elementary charge.
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Charge from one object will be shared with a neutral object if touched on the outside
Charge will be completed given away when charged object is touched inside another
Lightning Rods
• What property of charged objects explains
how they work?
• page 493 #17, 18, 19, 20, 28, 34