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PHYSICS 112
Dr. Anatoli Frishman
[email protected]
Physics
Mechanics Thermal properties
Electromagnetism
•Electrostatic
•Electric current
•Magnetism
Condensed Mater
High energy
Optics
Atoms & particles
•Geometrical optics
•Wave optics
Biophysics
Classical physics
Quantum physics
Relativistic physics
Quantum relativistic physics
Electromagnetism
(electric and magnetic phenomena)
This is about: electric charges, electromagnetic forces, and
electromagnetic fields
I. Electrostatics
This is about: non-moving electric charges, electrostatic forces, and
electrostatic fields.
(With very good approximation, electrostatics could be applied to slow
moving charges. Slow means that the speed of the considered charge is
much smaller then speed of light: v<<c)
1. Electric charge
1a. Qualitative description
•There are two and only two types of electric charges
•Charges of the same type repel, and charges of different type attract
(this is already qualitative description of electrostatic forces)
•These two types are referred to as positive and negative (+q and –q)
•Charges can be treated algebraically, and the net amount of electric charges
in an isolated system is conserved (is not changed in any process). This is
the law of conservation of electric charges
1b. Elementary charge:
e  1.6 10 19 C
1c. Electric properties of different materials
(very brief, qualitative description)
•Microscopic picture (atom)
•Insulators
•Conductors
•Semiconductors
•Superconductors
1d. “Games” with electric charges
•Charging by contact
•Charging by induction
•Electroscope
•Electrometer
The electroscope
disk
Positive
Negative
Neutral
Gold leaves
(or vane)
Charged rod
Positive
Inducted
charge
Negative
Neutral
Inducted
charge
repulsion
Charged rod
(closer)
Positive
Negative
Neutral
Stronger
repulsion
If we ground the electroscope while the rod is
there, the charges in the electroscope that were
“escaping” from the rod flow to the ground.
Positive
Negative
Neutral
No
repulsion
Then we cut the grounding…
Positive
Negative
Neutral
No
repulsion
And remove the rod…
The electroscope is now charged.
The charge spreads now all over the object.
Electroscope charged by induction
Positive
Negative
Neutral
Repulsion
2. Electrostatic forces (Coulomb’s law)
F k
k
1
40
Q1Q2
r2
Q1
 8.99 109 Nm 2 / C 2
Units:
r
Q2
 0  permittivi ty constant
Q
I
 Q  It
t
[Q ]  1C  1A 1s
[ I ]  1A
Example:
Q1  2.0 10 6 C
Q2  3.0 10 6 C
r  0.10m
F ?
F  9.0 109 Nm2 / C 2
F  5.4 N
2.0 10 6 C  3.0 10 6 C
0.1m2
Coulomb’s law in vector form:

F12
Q1
r
Q2
Q1 and Q2 have the same sign
Q1Q2 >0
Principle of superposition:



Q1Q2 r12
F12   F21  k 2
r
r

F21
Q1

F12
r

F21
Q2
Q1 and Q2 have opposite signs
Q1Q2 <0

 
Fnet  F1  F2  ...
Example:
Q1  1.0 C
Q1

F12
Q2  2.0 C
r

F13
Q2



F1  F12  F13
Q3
r
F1  F12  F13
Q3  12.0 C
r  0.10m
F1  ?
F12  k
Q1Q2
F13  k
Q1Q3
r
2
2r 
2
 9.0  10 9 Nm 2 / C 2
 9.0  10 9 Nm 2 / C 2
1.0  10 6 C  2.0  10 6 C
0.1m
2
1.0  10 6 C  12.0  10 6 C
2  0.1m
F1  F12  F13  1.8 N  2.7 N  0.9 N
F1  k
Q1Q2
r
2
k
Q1Q3
2r 
 9.0 10 Nm / C
9
2
2
2
k
Q1
r
2
1.0 10 6 C
0.1m2
Q2 
Q3
4

12.0 10 6 C
2.0 10 C 
 0.9 N
4
6
2
 1.8 N
 2.7 N
Q
Example:
Q  1.0 C
a  0.10m

F ?
Ftot 
Q
a
Q
Q

F2
2 F1  F3 

F3
Q2
F1  F2  k 2
a
Q2
F3  k 2
2a

  
Ftot  F1  F2  F3

F1
Q2
Q2
1  Q2

2k 2  k
  2  k 2
2
a
2a
2 a


1
1.0 10 C

Ftot   2    8.99 109 Nm 2 / C 2
2
0.10m 2


-6

2
 1.7 N
Example: Compare the gravitational attraction and the electric repulsion of two electrons
e  1.6  1019 C
e2
FE  k 2
r
m  9.1  10 31 kg



m2
FG  G 2
r
19

2
FE
9.0  10 Nm C 1.6  10 C
ke


2
FG Gm
6.7  10 11 Nm 2 kg 2 9.1  10 31 kg
2

9
2
2

2
 4.2  10 42
Big!
Example: One of your friends can resist a force of 100 lb (450 N) with his arms apart.
You give him two charged balls with charges Q and Q to hold on each hand.
How large a charge Q can he hold outstretched?
Q2
F k 2
r
Qmax
Q
-Q
r ~ 1.5 m
r2
 Fmax
 3.35  10 4 C
ke
-31
9.1

10
kg
1
electron
-15
3.35  104 C 


2

10
kg
-19
1.6  10 C 1 electron
Less than a cell in your body!