DEPARTMENT OF PHYSICS AND NANOTECHNOLOGY
SRM INSTITUTE OF SCIENCE AND TECHNOLOGY
18PYB101J-Electromagnetic Theory, Quantum Mechanics, Waves
and Optics
Module I Lecture-2
Electric Field and Electrostatic Potential, Volume, Surface
Charge and Line Charge, Point Charge, Gauss Law and
Applications
18PYB101J Module-I Lecture-2
Electric field: Electric field is defined as the electric force per unit charge
Electric charges affect the space around them. The space around the charge within
which its effect is felt or experienced is called electric field.
Electric field Intensity (or) Strength of the electric field(E)
The electrostatic field intensity due to a point charge qa at a given point is defined
as the force per unit charge exerted on a test charge qb placed at that point in the field.
18PYB101J Module-I Lecture-2
Electrostatic Potential (V)
As in the study of mechanics, it is useful to think in terms of the work done by
electrical forces and the potential energy in electric charges to understand the behaviour
of electric charges. Just as the heat flows from a higher temperature to lower
temperature, water flows from higher level to lower level and air flows from higher
pressure to lower pressure, electric charge flows from a body where electrical level is
more to a body where it is less. This electrical level is called electric potential.
The electric potential is defined as the amount of work done in moving unit
positive charge from infinity to the given point of the field of the given charge against
the electrical force.
Unit: volt (or) joule / coulomb
18PYB101J Module-I Lecture-2
The electric potential at any point is equal to the work done in moving the unit
positive charge from infinity to that point.
Therefore Potential
18PYB101J Module-I Lecture-2
The electric potential at any point is equal to the work done in moving the unit
positive charge from infinity to that point.
Therefore Potential
18PYB101J Module-I Lecture-2
Electric Field due to Point Charge
Let P be a point lying in vacuum at a distance r form a point charge q lying at O. Let a
test charge q0 be placed at P. According to Coulomb’s Law, the force acting on q0 due
to q is
F = qq0/4πε0r2
The EF at a point P is, by definition, given by the force per unit test charge.
E = F/q0
E = q/4πε0 r2
The direction of E is along the line joining O and P, pointing outward if q is positive
and inward if q is negative.
18PYB101J Module-I Lecture-2
Charge density
If the charge is distributed continuously in medium called Charge density
Line Charge density
If the charge is spread out along a line, with charge per unit length λ, then dq = λdl
Thus, the electric field of a line charge is
E = 1/4πε0 ∫ (λ/r2 ) dl
18PYB101J Module-I Lecture-2
Surface Charge density
If the charge is smeared out over a surface, with charge per unit area σ, then dq = σda
For a Surface charge
E = 1/4πε0 ∫ (σ/r2 ) da
Volume Charge density
If the charge fills a volume, with charge per unit volume ρ, then dq = ρdτ
Thus, the electric field of a line charge is
E = 1/4πε0 ∫ (ρ/r2 ) dτ
18PYB101J Module-I Lecture-2
Gauss theorem (or) Gauss law
This law relates the flux through any closed surface and the net
charge enclosed within the surface. The electric flux through a closed
surface is equal to the 1/ε0 times the net charge q enclosed by the
surface.
or
18PYB101J Module-I Lecture-2
Electric field due to a uniformly charged sphere When the point P
lies outside the sphere
P is a point at a distance r from the centre O. We have to find the electric Field E at P.
Draw a concentric sphere of radius OP with centre O. This is the Gaussian surface. At
all points of this sphere, the magnitude of the electric field is same and its direction is
perpendicular to the surface. Angle between E and dS is zero. The flux through this
surface is given by
18PYB101J Module-I Lecture-2
Electric field due to a uniformly charged sphere When the point P lies outside the
sphere
∮E.ds = ∮Eds = E(4Πr2)
By Gauss’s Law
E(4Πr2) = q/ε0
E = 1/(4Π ε0 )q/r2
Hence the EF at an external point due to a uniformly charged sphere is the same as if
the total charge is concentrated at its centre.
18PYB101J Module-I Lecture-2
Electric field due to an Infinite line of charge
Consider a uniformly charged wire of infinite length having a constant linear
charge density λ. Let P be a point at a distance r from the wire. Let us find an
expression for E at P. As a Gaussian surface, we choose a circular cylinder of radius r
and length l, closed at each end by plane caps normal to the axis. By symmetry, the
magnitude of EF will be the same at all points on the curved surface of the cylinder, and
directed radially outward. Also E and ds are along the same direction.
18PYB101J Module-I Lecture-2
Electric field due to an Infinite line of charge
Electric flux due to the curved surface = ∮E.ds = E(2Πrl)
Electric flux due to each plane face = 0 (E and ds are at right angle)
Therefore total flux through the Gaussian surface = φ = E(2Πrl)
The net charge enclosed by the Gaussian surface = q = λl
By Gauss law E(2Πrl) = λl/ ε0
E= λ/2Πε0r
18PYB101J Module-I Lecture-2
