The branch of physics which deals with electric effect of static charge is called
electrostatics.
Charge is a scalar quantity : It adds algebraically and represents excess or
deficiency of electrons
A body can be charged by means of (a) friction, (b) conduction, (c) induction, (d) thermionic
ionization or thermionic emission (e) photoelectric effect and (f) field emission
Conductor : Conductors are the material in which the outer most electrons are very loosely
bound, so they are free to move (flow). So in a conductor, there are large number of free electrons
To understand this, let’s have introduction to induction
Method
Step 1. Take an isolated neutral conductor..
When the metal is heated at a high temperature then some electrons
of metals are ejected and the metal becomes positively
charged.
On the basis of experiments Coulomb established the following law known as Coulomb's law :
The magnitude of electrostatic force between two point charges is directly proportional to the product of
charges and inversely proportional to the square of the distance between them
The electrostatic force is a two body interaction i.e. electrical force
The point where the resultant force on a charged particle becomes zero is
called equilibrium position
Electric field is the region around charged particle or charged body in which if
another charge is placed, it experiences electrostatic force.
Direction of electric field due to positive charge is always away from it while due
to negative charge, always towards it.
List of formula for Electric Field Intensity due to various types of charge distribution
Line charge of finite length : Derivation of expression for intensity of electric field at a point due
to line charge of finite size of uniform linear charge density ?. The perpendicular distance of the
point from the line charge is r and lines joining ends of line charge distribution make angle ?1 and
?2 with the perpendicular line
ELECTRIC FIELD DUE TO AN INFINITELY LARGE, UNIFORMLY CHARGED SHEET
Derivation of expression for intensity of electric field at a point which is at a perpendicular distance
r from the thin sheet of large size having uniform surface charge density
Electric field due to uniformly charged spherical shell
Finding electric field due to a uniformly charged spherical shell
Steps of integration : From above integral
Derive an expression for electric field due to solid sphere of radius R
and total charge Q which is uniformly distributed in the volume,
at a point which is at a distance r from centre for given two cases
In electrostatic field, the electric potential (due to some source charges) at a point P is
defined as the work done by external agent in taking a unit point positive charge from a
reference point (generally taken at infinity) to that point P without changing its kinetic
energy
Electric Potential due to various charge distributions are given in table
Potential due to a point charge
Potential at the centre of uniformly charged ring :
Potential due to the small element dq
A disc of radius 'R' has surface charge density (charge/area) We have to find potential at its axis, at
point 'P' which is at a distance x from the centre
Derivation of expression for potential due to uniformly charged hollow sphere of radius R and
total charge Q, at a point which is at a distance r from centre for the following situation
Potential Due To Uniformly Charged Solid Sphere
The potential difference between two points A and B is work done by external agent against
electric field in taking a unit positive charge from A to B with no change in kinetic energy
between initial and final points ie
Potential difference in a uniform electric field
Potential difference due to infinitely long wire :
Derivation of expression for potential difference between two points, which
Derivation of expression for potential difference between two points, having
separation d in the direction perpendicularly to a very large uniformly charged
thin sheet of uniform surface charge density
Definition : If potential of a surface (imaginary or physically existing) is same throughout, then such surface
is known as an equipotential surface
The electrostatic potential energy of a point charge at a
point in electric field is the work done in taking the charge
from reference point (generally at infinity) to that point
without change in kinetic energy
ELECTROSTATIC POTENTIAL ENERGY OF A SYSTEM OF CHARGES
Finding P.E., (Self Energy) of a uniformly Charged spherical shell :-
For this, lets use method 1 : Take an uncharged shell. Now bring charges one by one from infinity to
the surface fo the shell. The work required in this process will be stored as potential Energy
Def: Energy density is defined as energy stored in unit volume in any
electric field. Its mathematical formula is given as following
RELATION BETWEEN ELECTRIC FIELD INTENSITY AND ELECTRIC
POTENTIAL
If two point charges, equal in magnitude ‘q’ and opposite in sign separated by a
distance ‘a’ such that the distance of field point r>>a, the system is called a
dipole. The electric dipole moment is defined as a vector quantity having magnitude
p = (q × a) and direction from negative charge to positive charge
As the direction of electric field at axial position is along the dipole moment
Electric Potential due to a small dipole
Dipole in uniform electric field
Dipole is placed along electric field
Dipole in non-uniform electric field
ELECTRIC LINES OF FORCE (ELOF)
The line of force in an electric field is an imaginary line, the tangent to which at any point on it represents
the direction of electric field at the given point
Consider some surface in an electric field E
Let us select a small area element
This law was stated by a mathematician Karl F Gauss. This law gives the relation between
the electric field at a point on a closed surface and the net charge enclosed by that
surface. This surface is called Gaussian surface. It is a closed hypothetical surface. Its
validity is shown by experiments. It is used to determine the electric field due to some
symmetric charge distributions.
Since, electric field due to a shell will be radially outwards.
So lets choose a spherical Gaussian surface Applying
Gauss`s theorem for this spherical Gaussian surface
Electric field due to solid sphere having uniformly distributed charge
Q and radius R
Electric field due to infinite line charge having uniformly
distributed charged of charge density
Electric field due to infinitely long charged tube having
uniform surface charge density and radius R
E due to infinitely long solid cylinder of radius R having uniformly
distributed charge in volume volume charge density
Conductors are materials which contain large number of free electrons which can
move freely inside the conductor
Suppose we have a conductor and at any 'A', local surface charge
density We have to find electric field just outside the conductor
surface.
Suppose a conductor is given some charge. Due to repulsion, all the charges
will reach the surface of the conductor. But the charges will still repel each
other. So an outward force will be felt by each charge due to others. Due to
this force, there will be some pressure at the surface, which is called electrostatic
pressure
Some other important results for a closed conductor
Potential on both spherical shell becomes equal after joining. Therefore
