1. No category

PPT No. 6
* Electric
Monopoles
* Electric Dipoles
* Field of a Dipole
* Couple and Force on a Dipole
• Energy of a Dipole
* Force on Charged Conductor
* Energy of Electrostatic Systems
Electric Monopoles, Dipoles
Electric Monopole
An isolated single charge can be called
an "electric monopole".
Electric dipole
Equal positive and negative charges placed
close to each other constitute an electric dipole
Electric Quadrupole
Two oppositely directed dipoles close to
each other are called an Electric Quadrupole
Electric Dipoles
An electric dipole is
a separation of positive and negative charges.
The simplest example of electric dipole is
a pair of electric charges of equal magnitude but opposite sign,
separated by some, usually small distance
A permanent electric dipole is called an electret
Electric Dipoles
A physical dipole consists of
two equal and opposite point charges:
in the literal sense, two poles.
Its field at large distances
(distances large in comparison to the separation of the poles)
Depends almost entirely on the dipole moment.
Electric Field of a Dipole
The electric field of an electric dipole is calculated by
the vector sum of the point charge fields of the two charges:
The electric field from a dipole can be found from
the gradient of the potential where
the Electrostatic potential at position r
due to an electric dipole at the origin is given by:
is a unit vector in the direction of r',
p is the (vector) Dipole moment, and
ε0 is the Permittivity of free space
Moment of a Dipole
Dipoles can be characterized by
their Dipole moment.
The electric dipole moment is
a measure of the separation of
positive and negative electrical charges
in a system of charges.
It is a vector quantity.
The electric dipole moment is denoted by p
Moment of a Dipole
In the simple case the electric dipole moment p is defined
for a pair of opposite point charges of magnitude q
(one with charge + q and other with charge − q) as
the strength (magnitude) of each charge q multiplied by
the separation (distance) d between them:
The direction is defined from
the negative charge to the positive charge.
Thus, the electric dipole moment vector p
points from the negative charge to the positive charge.
Couple and Force on a Dipole
When a dipole is placed in an electric field E,
equal but opposite forces act on each side of the dipole
giving rise to a Torque τ:
Torque τ = E q d sin θ
Couple and Force on a Dipole
Electric Dipole moment p is given by
p = qd
(in coulomb-meters),
Torque τ = E q d sin θ
τ =pXE
Thus Torque can be expressed as
a vector product and
its direction is given by the right hand rule
Electric Dipole and Torque
Fig. Electric Dipole and Torque
Energy of an Electric Dipole
Fig Forces on dipole kept in an electric field
Energy of an Electric Dipole
The torque resulting from
two equal and opposite charges q
tends to align the electric dipole having Dipole moment p
in the direction of applied field E,
since it is the configuration having the lowest energy.
To take it from this state of lowest energy,
work has to be done against the electric field.
It is stored as potential energy U given by
Energy in the Electric Field
The electric field stores energy.
The energy density of the electric field is given by
ε is the permittivity of the medium in which the field exists
E is the electric field vector.
Energy in the Electric Field
The total energy stored in the electric field E
in a given volume V is
Where
dV is the differential volume element
ε is the permittivity of the medium