The
Coulomb’s force is valid while the order of magnitude of r is between 1017 m and 107 m .
Gravitational vs. Electrical Force
q1 + m1
r
- q2 m2
Felec k Fgrav
F Fi
F1
q
q1
F
F2
q2
Parallelogram rule of vector addition
Example

q0, q1, and q2 are all point charges where q0 = -1 mC, q1 = 3 mC, and q2 = 4 mC. Their locations are shown in the diagram. What is the force acting on q0?
q1 q2
r2 Fgrav G m1m2
For an electron:
q 1.6 10
C
m 9.110 kg
31
Felec 4.17 1042 Fgrav
What happens when you consider more than two particle charges?
If q1 were the only other charge, we would know the force on q due to q1. If q2 were the only other charge, we would know the force on q due to q2.

The
The
The
Coulomb’s force is a central force（有心力）.
Comments on Coulomb’s Law…
q1q2 q1q2 ˆ ˆ F12 k 2 r r 12 2 12 r 4 0 r
The
exponent, 2, in Coulomb’s Law has been shown to be accurate to 1 part in 1016 [that is, 2 11016 ].
ˆ r 12 is a unit vector
pointing from q2 to q1
Comments on Coulomb’s Law
q1q2 q1q2 ˆ ˆ F12 k 2 r r 12 2 12 r 4 0 r
This
force has same spatial dependence as the gravitational force. strength of the force between two particle charges is determined by the charge and the separation between them. Coulomb’s Law applies exactly only to point charges in vacuum.
Chapter 1
+
Today’s Agenda

Electric Charges（电荷） Coulomb’s Law

The Electric Field（电场强度）

Electric Field of a Point Charge
Electric Field of a Bunch of Charges

Is it like particle（质点）which we mentioned in Mechanics?
Coulomb’s Law
(Inverse-square force law for electricity)
In an inertial frame of reference, the force between two stationary point charges in vacuum is in the inverse ratio of the squares of the distance between the two particles and is proportional to the product of the charges q1 and q2. It’s attractive if q1 and q2 are of opposite sign and repulsive if same sign.
q1
r
q2
q1 q2 F k 2 r
Coulomb’s Law…
q1q2 q1q2 ˆ ˆ F12 k 2 r r 12 2 12 r 4 0 r
F12
SI Units:
• r in meters (m)
q1
+
ˆ12 r
r
q2
+
F21
k 9.0 109 N m 2 /C 2 (k : the Coulomb constant )
Properties of Electric Charges…

Charge is quantized (电荷的量子性). Electric charge always occurs as some integral multiple of some fundamental unit of charge, e = 1.602×10 -19 C. Thus q = N e. An important property of electric charges discovered by Robert Millikan in 1909.
?
?
? rosin rod
glass rod
Electric Charges…

If two charged rosin rods (or two charged glass rods) are brought near each other, the rosin rod (or glass rod) is repelled by the other rosin rod (or glass rod).

Unlike charges attract; like charges repel (异种电 荷相吸，同种电荷相斥).
This is an important property of electric charges.
Properties of Electric Charges…

Conventions suggested by B.Franklin (1706-1790，美 国独立宣言的起草人之一，避雷针的发明人 ): The electric charge on the glass rod is called positive. The electric charge on the rosin rod is called negative.
?
?
? rosin rod
rosin rod
Properties of Electric Charges…

Du Fay’s explanation (法国科学家杜菲的解释) :

There exist two kinds of charges in nature. One is vitreous(玻璃型）, the other is resinous(松脂型).
+
proton
electron
neutron
Quark Model
+ proton neutron
A proton is made up of two up quarks and one down quark.
(+2/3 e )+ (+2/3 e )+( -1/3 e)= +e
A neutron is made up of two down quarks and one up quark.
+
+
+
glass rod
Franklin’s famous kite experiment
rosin rod
Properties of Electric Charges…

Charge is conserved (电荷守恒). For an isolated system（孤立系统）, the algebraic sum of the quantity of the positive and negative charges keeps constant at any time. An important property of electric charges.

What is the force on q when both q1 and q2 are present??
F1
q
q1
q1
q
F2
q
?
q2
q2
More than two particle charges…

Just as in mechanics, we have the Superposition principle of Coulomb’s force (it’s an experimentally observed fact) : The TOTAL FORCE on a particle charge is just the VECTOR SUM of the individual forces due to other particle charges.