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Electric Field
Let's take a single electric charge, Q, and put it somewhere. The
space around it is different from the space without charge. We have
created a situation in which we could have an electric force. All we
have to do is bring in a second charge, q, to feel the force. Without
q, there is no force ....but we still have the condition that we could
have a force. We say that the space around charge contains
How to measure/find the strength (magnitude and direction)
of electric field at particular location P due to charge Q?
A test charge, q, placed at P will experience an electric
force, F - either attractive or repulsive.
Definition of electric field, E, at a point P distance r away from Q.
The magnitude of the electric field is
defined as the force per unit charge.
As F contains q, E DOESN’T
depend on q at all, only on Q.
Electric field at any point P in space is always
in the direction of the force on a positive test
charge if it were placed at the point P.
E  
The other way around:
If you know electric field E at a point where you place
a charge q, that charge will experience the force F:
Electric field of a charged particle/point charge
A charged particle Q creates an electric field.
E Field independent
◊ magnitude E  q = k r2
of test charge
the same value on the sphere of radius r around
◊ direction – radially outward or inward
Q=1.6x10-19 C
r = 1x10-10 m
E = 9109 1.610
= 2.91011 N/C
q positive test charge
(to the right)
Say the electric field from an isolated point charge has
a certain value at a distance of 1m. How will the electric
field strength compare at a distance of 2 m from the
It will be ¼ as much – inverse square law for force
between two charges carries over to the electric field
from a point charge.
We use “Electric Field Lines” to visualize el. field.
Convention / agreement
Direction indicates direction in which a positive test
charge would be pushed – direction of the force!!!.
321011 N/C
Electric Field of a Point Charge
2.91011 N/C
This is becoming a mess!!!
Electric Field Lines
1. Density gives strength
# lines proportional to Q
lines never cross!
2. Arrow gives direction
Start on +, end on -
So always point away from
+ charges, towards – charges…
Denser lines - stronger field
el. field decreases with distance
more lines revels stronger
field due to greater charge
Electric field lines can never cross. If they crossed, that
would mean that a charge placed at the intersection,
would be accelerated in TWO directions at once! This is
impossible! If two sources are creating electric fields in the
same place, we have to add the two vectors and get a
resultant vector representing the NET ELECTRIC FIELD.
What is the direction of the electric field at point C?
1) Left
2) Right
Away from positive charge (right)
Towards negative charge (right)
Net E field is to right.
What is the direction of the electric field at point A?
1) Up
2) Down
3) Left
4) Right
5) Zero
What is the direction of the electric field at point B?
1) Up
2) Down
3) Left
4) Right
5) Zero
What is the direction of the electric field at point A, if the
two positive charges have equal magnitude?
1) Up
2) Down
3) Left
4) Right
5) Zero
Electric field
of a capacitor
Uniform electric field (the one that has constant magnitude and direction
is generated between two oppositely charged parallel plates. Edge effect
is minimazed when the length is long compared to their separation.
Electric field of a charged conducting sphere in
electrostatic equilibrium
Electric field outside a charged sphere (evenly distributed
charge q over surface) at distance r from its center is the same
as if the charge q is concentrated at the center of the sphere:
at the surface
What is electric field inside the sphere?
OK. Let’s start. In general if you have many charges you
have to find el. field of each of them and then add them up
as vectors to get net el. field at certain point. So imagine a
solid!!!!!!!!! Good luck.
Different approach:
Conductor is in electrostatic equilibrium
when there is no net motion (flow ) of
charge within a conductor or on its surface.
• Conductor  electrons free to move
• charges in electric field feel the force F = Eq
• only free electrons can move in the conductor so they will move until
 E = 0 inside a conductor
if not then electrons would respond to its presence and be accelerated
within the conductor. And that is not conductor in electrostatic equilibrium.
 If such conductor has excess charge, it resides
entirely on the conductor’s outer surface running away
from each other as far as possible. El. field is still zero
everywhere inside the conductor.
Therefore, electric field of charged conducting
sphere in electrostatic equilibrium is:
at the surface
El. field just outside a charged conductor is
perpendicular to the conductor’s surface.
if not
 Charge tends to accumulate where the curvature is the greatest
(sharp points).
The fact that pointed objects create
strong electric fields if charged is the
reason for the shape of lightning rod.
You’ll see.
Summary: Conductors in electrostatic equilibrium
 no net motion (flow) of charge within a conductor . Then:
 El. field is zero everywhere inside the conductor
 If such conductor has excess charge, it resides entirely on the
conductor’s outer surface. El. field is still zero everywhere inside the
 El. field just outside a charged conductor is perpendicular to the
conductor’s surface.
 Charge tends to accumulate where the radius of curvature is
smallest (sharp points).
Electrical Shielding
 Electric field is zero inside conductor, regardles how strong
the electric field is outside.
 Even more: electric field inside metal cavities is zero,
regardles what’s going outside - so put electrical equipment in
metal boxes. Outside may be very strong fields and high
charges, but the charges on the metal surface rearrange to give
0 inside.
 This is why if lightning hits a car and you’re inside, you’re
safe, at least if it is not too strong ot make everything melt.
Electrons from the lightening bolt mutually repel and spread over
the outer surface. Although the electric field they set up maybe
great outside the car, the overall electric field inside the car
practically cancels to zero.
 Radio signals cannot penetrate through a metal enclosure
(mobile in an elevator)
 The metal bars (rebar) that reinforce the concrete in walls
can interfere also
Electrostatic shielding
• The effect of the high
voltage on the van
de Graff generator
stops on the outside
of the metal cage 
Homer is SAFE!
Lightning – great weapon of the Gods
• causes 80 million dollars in damage each year
in the US
• kills ~ 85 people a year in the US
• is all over in a thousandth of a second
• carries up to 200,000 Amperes (currant)
• temperature of a lightning bolt can reach
– 5x hotter than the surface of the
• causes the thunder!
development of a lightning bolt
1. step: Positive and negative charges separate.
A cloud becomes positively charged at the top
and negatively charged at the bottom. Reasons
for this charge distribution are complex and
only partially understood.
2. step: As the negative charges collect at
the bottom of the cloud it forces the
negative charges in the ground to be
forced away from the surface.
This leaves the ground positive.
If attractive force is large enough electrons
will leap from negative region downward
from the cloud to the ground.
+++ +++
+++ +++
+++++++ +++
3. step: As the electrons approach the earth, el.
field just above the surface becomes so
intense that it ionizes atoms and molecules in
the air. An intense flash of light is produced.
4. step: When first breakdown occurs, negative
charge in the column farther above the earth
can rush down through the region of ionized
Now that flow of electrons originated farther
above the earth causes a flash of light. That
way flash appears to move up.
The rapidly moving electrons excite the air along the path so
much that it emits light. It also heats the air so intensely that it
rapidly expands creating thunder.
One thing to notice is that the positive charges that make up both the
cloud and the ground do not move. Even the positive streamer
launched by the ground (in the animation) is really only made up of
positively charged air particles because the electrons left the particle.
Electrons in atoms orbit the nucleus well defined orbits
called stationary states. By absorbing energy atom can
be raised to higher energy level called excited state.
When excited electron jumps back to a lower level it
emits photon.
At ordinary temperatures and when not in strong electric filed most
atom are in the ground state. But if the temperature is high and/or
electric field very strong the air will turn into plasma. The light is
generated when the stripped electrons in the plasma recombine
with the ionized ions. The probability of recombination process is
pretty high, so the time for the recombination to occur is short. The
streaks of light from the lightening fade away almost immediately.
When a meteor shower enters the very high regions of the
atmosphere, streaks of light last for as long as 2 – 3 seconds
before fading. Because the probability of freed electrons finding an
ionized atom with which to recombine is very low (pressure and
density are low - atoms are relatively far apart).
Lightening Rods
+ + +
Place rod above a building, and connect it to
ground. Then the point of the rod picks up
electrons from the air (“leakage”), so prevents
large build up of + on the building, hence
decreasing chance of a lightning strike.
+ +
+ +
But even if there is a lightning strike (if leakage not
enough), the electricity goes through rod to
ground, rather than through building.
While enjoying the Sequoia National Park from
a lookout platform, this woman found her hair
rising from her head. Amused, her brother
took her photograph. Why should she run for
Five minutes after they left, lightning struck the
platform, killing one person and injuring seven.

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