Download Electric field of a spherical shell Q

Hw: All Chapter 5 problems and exercises
"Gravitation cannot be held responsible for
people falling in love.“ Albert Einstein
Outline
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Applications of Gauss’s Law
The single Fixed Charge
Field of a sphere of charge
Field of a spherical shell
A Line of Charge
Conductors and Insulators
The electric field of a conductor
The field in the cavity of a conductor;
Faraday’s Cage
Gauss’s Law
The total flux of electric field out of any
closed surface is equal to the charge
contained inside the surface divided by  0 .
  Qenclosed
 E  dS 
S
0
Electric field of a ball of charge
Q
1
Q
rR E
40 r 2
rR
1
rQ
E
40 R 3
Electric field outside of a charged sphere is exactly the
same as the electric field produced by a point charge,
located at the center of the sphere, with charge equal to the
total charge on the sphere.
Electric field of a spherical shell
Q
The field outside the shell is like that of a point charge,
while the field everywhere inside the shell is zero.
Electric field of a line of charge


E
20 r
Conductors and insulators
Charges reside at the surface of the conductor
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Conductor
E=0
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Solid conducting sphere with charge Q
A
E
r A E0
rA E
V
A
r
1
Q
40 r 2
1 Q
rA V 
40 A
1
Q
40 A
r
rA V 
1 Q
40 r
Ionization and corona discharge
There is maximum potential to which a conductor in air
can be raised because of ionization.
Em  3106
V
m
Vm
 Em
R
Small potentials applied to sharp points in air produce
sufficiently high fields just outside the point to ionize the
surrounding air.
A lightning rod has a sharp end so that lightning bolts will pass through a
conducting path in the air that leads to the rod; a conducting wire leads from the
lightning rod to the ground.
The metal mast at the top of the Empire State
Building acts as a lightning rod. It is struck by
lightning as many as 500 times each year.
Benjamin Franklin
"For my own part I wish the Bald Eagle had not been chosen the Representative of
our Country. He is a Bird of bad moral Character. He does not get his Living
honestly. You may have seen him perched on some dead Tree near the River,
where, too lazy to fish for himself, he watches the Labour of the Fishing Hawk; and
when that diligent Bird has at length taken a Fish, and is bearing it to his Nest for
the Support of his Mate and young Ones, the Bald Eagle pursues him and takes it
from him.
"With all this Injustice, he is never in good Case but like those among Men who live
by Sharping & Robbing he is generally poor and often very lousy. Besides he is a
rank Coward: The little King Bird not bigger than a Sparrow attacks him boldly and
drives him out of the District. He is therefore by no means a proper Emblem for the
brave and honest Cincinnati of America who have driven all the King birds from our
Country....
"I am on this account not displeased that the Figure is not known as a Bald Eagle,
but looks more like a Turkey. For the Truth the Turkey is in Comparison a much
more respectable Bird, and withal a true original Native of America... He is besides,
though a little vain & silly, a Bird of Courage, and would not hesitate to attack a
Grenadier of the British Guards who should presume to invade his Farm Yard with
a red Coat on."
--Benjamin Franklin, in a letter to his daughter
First exam Tuesday, February 16
105 Heldenfels
Sections 807 and 808 start at 7 pm
Sections 809 and 523 start at 8:10 pm
BRING YOUR STUDENT ID!
No calculators and cell phones
What is included?
Chapters 1-4
Have a great day!
Be prepared for the test!