ELECTROSTATIC POTENTIAL AND CAPACITANCE
SATHEESH KUMAR B
PGT PHYSICS
JNV ERNAKULAM
Electric potential at a point due to a point charge. �
Electric Potential at a point in the electric field is defined as the work done in moving (without any acceleration) a unit positive charge from infinity to that point against the electrostatic force.
Electrostatic potential difference between two points is defined a the work done in bringing a unit positive charge from one point to another.
Electric Potential Difference between any two points in the electric field is defined as the work done in moving (without any acceleration) a unit positive charge from one point to the other against the electrostatic force irrespective of the path followed.
The S.I Unit of electric potential is volt(V).
One volt
Electric potential at a point is one volt if one joule of work is done in moving one coulomb of positive charge from infinity to that point in the electric field.
POTENTIAL AT A POINT DUE TO A POINT CHARGE�
Q
p’
p
The negative sign appears because for ∆r′ < 0, ∆W is positive .
POTENTIAL DIFFERENCE BETWEEN TWO POINTS
The potential difference between two points is independent of the path through which it is displaced. But depends only on the initial and final positions.
The electric field is conservative in nature, because the work done by the electric field is independent of the path.
or
The work done by the electric field over a closed path is zero.
Conservative nature of electric field
The graph showing the variation of potential and field due to a point charge with distance.
Potential at a point due to two point chrges
O
P
Q
POTENTIAL AT A POINT DUE TO AN ELECTRIC DIPOLE� �
AN = a sinθ and ON= a cosθ
+q
-q
P
r1
r2
r
N
O
a
a
M
A
B
θ
+q
-q
P
r1
r2
r
N
O
a
a
M
A
B
θ
ELECTRIC POTENTIAL ENERGY OF A SYSTEM OF CHRGES�
Potential energy of a system of charges is defined as the work done in bringing them from infinite separation to the present position.
Consider a system of two charges q1 and q2 separated by distance of r12 apart in free space. let the position vector of charges are r1 and r2 respectively.
Let us consider that these charges are kept initially at infinite separation. We can find the work done in bringing them from infinite separation to the present position.
q1
q2
r1
r2
Potential energy of a system of three charges
q2
Potential energy of a dipole in an external field
ϴ
Special cases:
Case.1
Case.2
Case.3
Equipotential Surface
An equipotential surface is a surface in which the electric potential at all points on the surface will be the same.
(1) Point charge
(2) Electric dipole
(3) Uniform electric field
Properties of equipotential surfaces
General relation between potential difference and field
ELECTROSTATICS OF CONDUCTORS
A conductor has free electrons. As long as electric field is not zero, the free charge carriers would experience force and drift. In the static situation, the free charges have distributed themselves so that the electric field is zero everywhere inside.
Inside a conductor electrostatic field is zero.
Electric field at the surface of a charged conductor
Capacitor and Capacitance
Different types of capacitors
Symbol of a capacitor
Capacitance of a parallel plate capacitor.
A Parallel Plate Capacitor is formed by two identical parallel conducting plate separated by a small distance of ‘d.
+Q + -Q� +� +� +� +� +� +----------d-----------� +� +� +� +� +
A + B
-
-
-
-
-
-
-
-
-
-
-
-
-
Capacitance of a parallel plate capacitor
Dielectrics and polarization
Dielectrics are non-conducting polar or non-polar substances.
If the centres of positive and negative
charges of a molecule do not coincide,
then it is a polar molecule.
If the centres of positive and
negative charge coincide each
other, it is a non polar molecule
In the polar molecule there will be a permanent dipole moment. But the net dipole moment of the substance becomes zero because of the random orientation of each molecule of the substance.
Polar molecule
Non-Polar molecule
Non-Polar substance in an external electric field
If a non-polar substance is placed in an external electric field, each molecule will change into dipoles in the direction of the external field and produce an induced field in the opposite direction.
Polar substance in an external electric field
If a polar substance is placed in an external electric field, each dipole molecule will align in the direction of the electric field and produce an internal field in the opposite direction.
Electric field inside a dielectric in an external electric field
In both polar and non-polar substances the internal field produced will be less than the external field and there by the net field becomes,
E = E0 - Ep
- +
- +
- +
- +
- +
- +
- +
- +
The effect of dielectric in a capacitor
When a dielectric is placed in between the plates of a parallel plate capacitor due to electric polarization, the electric field and hence the potential between the plates is decreased. Hence the capacitance of the capacitor is increased
-----------------d-------------------
+�+�+�+�+�+�+�+�+�+�+�+�+�+�++�+�+�+�+�
_�_�_�_�_�_�_�_�_�_�_�_�_�_�_�__�_�_
_
-----t----
Capacitance of the capacitor if the region between the plates is fully filled with the dielectric.
t = d
Energy stored in a capacitor
Combination of capacitors
Capacitors can be connected together in a circuit in two different ways, series combination and parallel combination.
(1)Series combination
(2)Parallel combination
C1 C2 C3
Series combination
Let us consider three capacitors C1, C2 and C3 connected in series with a voltage source ‘v’ as shown below.
If the Capacitors are connected in Series the same charge ‘Q’ will be reaching to all the capacitors and the potential ‘V’ is divided into V1, V2 and V3 across C1, C2 and C3 respectively.
C1 C2 C3
If these capacitors are replaced by an equivalent capacitance ‘Cs’ such that the voltage ‘V’ and the charge ‘Q’ remains the same, then
Series combination of n capacitors
Parallel combination
If the capacitors are connected in parallel, the potential difference across each capacitor will be same and equal to the source voltage V, but the charge is distributed as Q1, Q2 and Q3 so that the charge from the source
If these three capacitors are replaced by a single capacitance ‘Cp’ in such a way that the voltage ‘V’ and the charge ‘Q’ remains the same, then
Cp
Q = CpV (3)
From (2) and (3)
CpV = (C1 + C2 + C3) V
Cp = C1 + C2 + C3
Q = (C1 + C2 + C3) V (2)
Parallel combination of n capacitors
If ‘n’ capacitors are connected in parallel then
Cp = C1 + C2 + C3 + …………………+ Cn
i.e. The effective capacitance in parallel combination is equal to the sum of the individual capacitances.
If ‘n’ identical capacitors of each ‘c’ are connected in parallel, then
CP = nC