Coulomb’s Law
B.Kalaimathi, AP/ECE
Coulomb's Law
It states that "the electrostatic force between two electric charges is directly proportional
to the product of the charges and inversely proportional to the square of the distance
between them ".
If q1 and q2 are two point charges separated by a distance r, then the electrostatic force F
between the charges is given by
where k is a positive constant called 'Coulomb's constant'. This value depends on the
medium between the two charges.
(a) If the charges are in vacuum, then in SI Units,
where e0 is the permittivity of space.
The value of e0 = 8.854 x 10-12 C2/Nm2 which was obtained by experiments. Thus, K =
8.988 x 109 Nm2/C2.
Unit of Charge - Coulomb
The unit of charge is Coulomb and is denoted by C. One coulomb of charge, is that
charge which when placed one meter from another charge in vacuum experiences an
electrical force of repulsion of magnitude 9 x 109 N .
(b) If the charges are immersed in matter, then e0 is replaced by e, a
e is called
absolute electric permittivity of the dielectric medium.
Coulomb’s Law
B.Kalaimathi, AP/ECE
or relative permittivity . So Coulomb's law is written as
Vector form of Coulomb's Law
(a) If q1q2 > 0, that is either both q1 and q2 are positive or both are negative, then the
charges repel each other.
(b) If q1q2 < 0, that is if the charges are dissimilar, then the charges attract each other.
Coulomb’s Law
B.Kalaimathi, AP/ECE
Thus, Coulomb's law agrees with Newton's third law.
Electric field intensity
The strength of the electric field is measured using a quantity called the electric field
intensity. The greater the electrical field intensity the stronger the field. The electrical
field intensity (EE) is defined as:
The electric field intensity is the force on a unit positive charge placed at that point in the
field.
In a uniform field the electric field intensity is constant (the same at any point in the
field) while in a radial field the electric field intensity decreases as the distance from the
central charge increases.
Therefore for a radial field the electric field intensity distance d from a positive charge of
size Q coulombs is:
Radial field:
EE = (1/4πεo)Q/d2
For a uniform field between two parallel plates separated by a distance d and with a
potential difference V between them the field is:
Uniform field:
EE = V/d
the units for electric field intensity are Newtons per coulomb (NC-1).
Units for electric field intensity
Coulomb’s Law
B.Kalaimathi, AP/ECE
An alternative unit for electric field intensity may be derived as follows.
Since Joules = Volts x coulombs = Newtons x metres (J = VC = Nm) we can write NC-1
as [VC/m]C-1 = Vm-1. The electric field intensity may also be expressed in volts per
metre (Vm-1).
Using these units it is probably easier to get a feel of what electric field intensity is, the
change of voltage with distance (see later). The bigger the field the more rapidly does the
potential change with distance. Think about this if you are near a Van de Graaff generator
and your hair stands on end.
Example problem
Calculate the electric field at a distance of 2 m from a Van der Graaff generator carrying
a charge of 1.0x10-6 C. [This is roughly the charge you would expect on a 0.2 m diameter
sphere charged to 100 kV in air.)
Using and following equation and considering the charge as a point(!) :
EE = (1/4πεo)Q/d2
EE = (1/4πεo)1.0x10-6/22 = 9x109x1x10-6/4 = 2.25x1015 Vm-1.
Coulomb’s Law
B.Kalaimathi, AP/ECE
Point, Line, Surface and Volume charge distributions
The total space covered by any charge in dimensions is very small as compared to the
distance between the two charges from an observation point. That observation point can be taken
as a point charge.
In a continuous charge distribution, all the charges are closely bound together i.e. having very
less space between them. But this closely bound system doesn’t means that the electric charge is
uninterrupted. It clears that the distribution of separate charges is continuous, having a minor
space
between
them.
Types of continuous charged distributions:
1. Linear Charge Distribution
2. Surface Charge Distribution
3. Volume Distribution of charge
Linear Charge Distribution:
When the distribution of charge is uniformly along the line then it is called Linear Charge
Distribution. E.g. line making the circumference of a circle, straight line, etc.
It is denoted by symbol
.
= dq / dl. It is measured in Cm-1 .Lets take a small element having length dl of the line L.
The small amount of charge on this element is
dq=
. dl.
So the resultant force can be calculated by using the formula:
Total force on small charge elements by adding them vectorially is:
Surface Charge Distribution:
When the charge distribution is over a particular area then the distribution is called as Surface
charge distribution.
It is denoted by
.
Coulomb’s Law
B.Kalaimathi, AP/ECE
= dq / ds. It is measured in Cm -2 . Total force F on a small test charge q0 is due to surface
distribution of charge. It is shown below:
Volume Distribution of charge:
When charge is distributed over a certain volume i.e. over a sphere, over a cube etc, then it is
called Volume distribution of charge.
Symbol to represent it is
Charge per unit volume is:
= dq / dV.
Note: In all the three cases unit vector is a variable unit, directed from each point on a line,
surface or volume against the test charge q0. The values of different distributions,
,
,
may vary at different points.
The simple expression for the resultant force applied on a test charge
by n number of different point charges and the three kinds of charge distributions is the vector
sum of all the distinct forces.