Coulomb found out that each electric point charge exerts a mechanical force on the other, and this force exhibits five characteristics as follows:

1. The force is proportional to the product of the magnitudes Q1 and Q2 of the two electric charges.

2. Like charges repel each other while like charges attract each other.

3. The force is inversely proportional to the square of the distance between the two charges.

4. The force depends upon the medium in which the two charges are located.

5. The force always acts along the straight line joining the two point charges Q1 and Q2.

Mathematically:

**
**

in MKS :

**
k = (4pe _{o})^{-9}**

**
e _{o}
= permittivity of free space**

**
= (1/36p)
x 10 ^{-9 }F/m = 8.854 pF/m**

**
**

F = Force (N)

Q_{1}
and Q_{2} = charges (C)

1
coul = 6.25 x 10^{18} e

1
e = 1.6 x 10^{-19} coul

Note:

I. The distance R between the charge bodies Q_{1} and Q_{2}
must be large compared to the linear dimension of the bodies.

II. Q_{1} and Q_{2} must be static.

**If we have more than 2 point
charges, we can use the principle of superposition to determine the force on a
particular charge say Q _{1}.**

**
**

Electric Field Intensity is defined as the force per unit charge when placed in the electric field.

**
**

where:

Q_{T}
- test charge

E - electric field intensity (V/m)

a_{1t}
- unit vector in the direction of R_{1T}

**
**

**
**

**
Consider a filament
like distribution of volume charge density such as a very fine, sharp beam in a
cathode ray tube or a charged conductor of very small radius, we find it
convenient to treat the charge as a line charge of density
r _{L}
(C/m).**

** **

subs (2) and (3) in (1)

**
**

r - perpendicular distance of the line charge to the point

a_{r}
- direction of the perpendicular line connecting the line charge to the point

**
**

**
**This charge distribution may often be used to approximate that found on the
conductors of a strip transmission line or a parallel plate of capacitor.

At z = z plane:

dE_{x} and dE_{1x}, dE_{y} and dE_{1y} will
cancel each other

In general, E due to an infinite sheet of charge:

**
**

a_{r}
- direction of the smallest distance connecting the sheet of charge to the point
in consideration.

**·**
**
Electric Potential Voltage (Voltage Potential of Voltage)**

- amount of work, or potential energy, required to move a unit charge between two points.

-the presence of electric field between two points results to the voltage difference between them.

Consider a positive charge "q" in a uniform electric field parallel to the negative y-direction.

**F _{e} =
qE (**

**
F _{ext} =
-q(-Ea_{y})(dy a_{y}) (force
needed to move the charge in the +y direction)**

**dw = F _{ext}
**

**
dw = -q (-Ea _{y})(dya_{y})
= qEdy (work or
energy needed if a charge is movd a distance dy along ay)**

**·**
**
Differential electric potential (or differential voltage)**

**dv = dw/q = -E
****·
d(Joules/C or V)**

**·**
**
Potential difference between two points P2 and P1**

**(a) Electric Dipole**

**(b) Electric Field
Pattern**

** line
integral of around any closed contour is zero.**

**
Assume P _{1}
is the ground, V_{1}= 0 P_{1} =
¥**

** (Electric
potential at any point)**

**
**

let P_{1} = R and dl = dR a_{R}

_{
}

** (due
to a point charge)**

** (due
to several charges)**

** (due
to volume charge specified over a given volume v’)**

** (due
to surface charge specified over a given volume s’)**

** (due
to line charge specified over a given volume l’)**

**·**
**
Electric Field as a Function of Electric Potential**

**
dv = -E dl also
dv = ÑV
dl**

**
E = -ÑV
**

**·**
**
Electric Field of an Electric Dipole**

Electric Dipole consists of two point charges of equal magnitude and opposite polarity, separated by a small distance

since d<<R

**
assumptions: R _{1}||R_{2}
\R_{2}
– R_{1 }@
dcosq
**

**
R _{1}R_{2 }
@
R^{2}**

**
qdcosq
= qd ·****
a _{R} = p **

_{
}

d – distance vector from –q to +q

a_{R}
– unit vector pointing from the center of the dipole toward the observation
point P.

**
P**
= qd – dipole moment of the electric dipole

**
from E = -ÑV**

**
(in spherical coordinates)**