Plus Two Physics Notes Chapter 2 Electric Potential and Capacitance is part of Plus Two Physics Notes. Here we have given Plus Two Physics Notes Chapter 2 Electric Potential and Capacitance.
|Text Book||NCERT Based|
|Chapter Name||Electric Potential and Capacitance|
|Category||Plus Two Kerala|
Kerala Plus Two Physics Notes Chapter 2 Electric Potential and Capacitance
Simplified Detailed Notes
It is defined as the work done in bringing a unit positive charge from infinity to that point against the electrostatic forces.
Electrostatic potential (V) =
Its SI unit is volt (V) and IV = I J/C.
It is a scalar quantity.
Electrostatic potential difference:
The potential difference between two points in an electric field may be defined as the amount of work done in moving a unit positive charge from one point to the other against the elecrostatic forces.
VB – VA = ; WAB
is work done in taking charge q0 from A to B against electrostatic forces.
The line integral of electric field from initial position A to final position B along any path is termed as potential difference between two points in the region of electric field.
ie., VB – VA =
Note: Work done on test charge by the electric field is independent of the path. Therefore the potential difference is also same for any path.
Potential Due to a Point Charge
Consider a point P lying at a distance r from a point charge q,
Note: Potential at a point due to +ve charge is positive and due to -ve charge is negative. When a +ve charge is placed in an electric field, it moves from higher potential to lower potential. For negative charge, it moves from lower to higher potential.
Potential Due to an Electric Dipole
Potential Due to System of Charges
Consider a system of charges q1,q2, q3 …….. qn with position vectors r1, r2, r3 ………. rn relative to some origin. Potential at P due to q, is V = V1+ V2+ V3 + ……. +Vn
Electrostatic potential due to a thin charged spherical shell. If the sphere carries charge q and has radius R, at any point P lying:
A surface which has same electrostatic poten-tial at every point on it is known as equipotential surface.
- No work is done in moving a test charge over an equipotential surface.
- Electric field is always normal to the equipotential surface at every point.
- Equipotential surfaces are closer together in regions of strong field and farther apart in the regions of weak field.
- No two equipotential surfaces can intersect each other.
Equipotential surfaces of Various charge systems
(i) Positive point charge:
(ii) Electric dipole
(iii) Two positive chareges
(iv) Unifrom Electric field
Non Unifrom Electric field (increasing)
Relation Between Electric Field and Electric Potential
E = –
Note: Here -ve sign shows that direction of electric field is from high to low potential, i.e., in the direction of decreasing potential.
Electrostatic potential energy: Electrostatic potential energy of a system of point charges may be defined as the amount of work done in assembling the charges at their location by bringing them from infinity.
For a system of two point charges:
Potential Energy in an External Field
(i) Of a Single Charge : Potential energy of a single charge q, at a point with position vector r, in an external field = qV(r).
(ii) Of a System of two Charges:
V(r1) = potential at r1 due to external field.
V(r2) = potential at r2 due to external field.
Note: The most common unit of energy in atomic physics is electron volt (eV)
leV = 1.6 x 10-19 J
Potential Energy of a Dipole
Two equal and opposite forces +q and -qform a couple τ =qE x 2asinθ – pEsinθ
If dipole is rotated through angle dd, small work done is, dW = τdθ = pE sinθ dθ
W = ∫dW = = pE (cosθ1 -COS θ2)
This work is stored as potential energy
U = pE(cosθ1 -COS θ2)
U = -pE cosθ = –. (if θ1 = 90°)
- Stable equilibrium (θ = 0°): – pEcosO = -pE
- Unstable equilibrium (θ = 180°): -pE cos180= +pE
Conductors and Insulators: Conductocs contain a large number of free charge carriers to conduct electricity, while insulators do not contain any free charge carnrers to conduct electricity.
Behaviour of Conductors in Electrostatic Field
- Net electrostatic field is zero in the interior of a conductor.
- On the surface of charged conductor electric field is normal to the surface.
- Net charge in the interior of a conductor is zero, and any excess charge resides on the surface.
- Potential is constant inside and on the sur¬face of a conductor.
- Electric field at the surface is proportional to the surface charge density.
Electrostatic shielding: It is the process which involves making a region free from any electric field is called electrostatic shielding. It is based on the fact that electric field is zero inside the cavity of a hollow conductor.
Note: This is the reason why we are advised to stay in a car rather than near a tree or in open space during thunderstorm and lightning!
The substances which are poor conductors of electricity are known as dielectrics. They are insulators.
There are two types. Polar dielectrics have a permanent dipole moment and non-polar dielectrics have no permanent dipole moment.
- In an External Electic Field: When a con-ductor is placed in an external electric field, the free charge carriers adjusts itself in such a way that the electric field due to charges’and external field cancel each other and the net field inside the conductor is zero.
In case of dielectrics however, the opposing field induced does exactly cancel the external field.
- A net dipole moment is developed, by an external field in either case, whether polar or non-polar dielectric. The dipole moment per unit volume is called polarisation and is denoted by P, P = X E ; where, X e is called electric susceptibility of the dielectic medium.
Capacitor and Capacitance
A capacitor comprises of two conductors separated by an insulating medium .
Capacitance of a conductor is the measure of its ability to hold electric charge. If charge Q is given to an insulated conductor, it leads to increase in its electric potential V, as Q ∝ V or Q = CV
Here the proportionality constant C is called capacitance of the conductor. Thus,
The SI unit of capacitance is farad (F).
Note: Capacitance does not depend on nature of its material and amount of charge existing on the conductor. It depends on shape, size and separation between conductors and also per-mittivity of the space between them.
Principle of a Capacitor: The capacitance of an insulated conductor is significantly in¬creased when an earthed uncharged conductor is kept near it. Such an arrangement is called a capacitor.
Capacitance of an Isolated Spherical Conductor
C = 4πε0r
The Parallel Plate Capacitor
Two large plane parallel conducting plates, separated by a small distance.
Note: When a dielectric of dielectric constant K is filled fully between the plates then,
If it is partially filled with a dielectric of dielectric constant K then,
t = thickness of dielectic
If it is partially filled with a conducting slab
t = thickness of conducting slab
Combination of Capacitors
1. Capacitors in Series
Potential difference across the combination is V = V1 + V2 +V3
Note: Charge on each capacitor will be same in series combination.
Potential is divided across the capacitors in the inverse ratio of their capacitances
Equivalent capacitance of n identical capacitors connected in series each of capacitance C is, Cs =
2. Capacitors in Parallel
The total charge on the combination:
q = q1 + q2 + q3
Note: The potential drop across each capacitor will be the same in parallel combination.
Total charge on the capacitors are divided in the ratio of their capacitances.
i.e., q ∝ C ⇒ q1 : q2 : q3 = C1 : C2 : C3
For parallel combiation of n capacitors,
Cp = C1 + C2 + ……..+ Cn
Equivalent capacitance of n identical capacitors connected in parallel combination is
Cp = nC
Effect of Dielectric on Various Parameters
When dielectric is inserted after battery is disconnected from the capacitor:
- Q = Q0
- E =
- C= KC0
- U =
When dielectric is inserted while battery is connected to the capacitor.
- Q = KQ0
- V = V0 (constant)
- E = E0
- C = KC0
- U = KU0
Energy Stored in Capacitor
Let a capacitor be charged to a charge Q’. If a small additional charge dQ’is given, the work
Redistribution of Charges
Consider two capacitors having capacitances C1 and C2 and charges Q1 and Q2. Let V1 and V2 be their potentials, respectively.
If these two conductors are joined by a thin conducting wire, then
Common potential =
Loss of energy, U = Ui – Uf (substitute above)
Van de Graaff Generator
A Van de Graaff generator is a device designed to create static electricity and make it available for experimentation.
Principle: The Van de Graaff generator works on the following two principles.
- Discharging action of sharp points i.e., electric discharge takes place in air or gases readily at pointed conductors.
- If the charged conductor is brought into internal contact with a hollow conductor, all of its charge transfers to the surface of the hollow conductor no matter how high the potential of the latter may be.
The high electric field at the pointed ends of comb C1, ionises the air near them. The +ve charges in air are repelled and got deposited on the belt through a corona discharge. The charges are carried upto C2. A similar corona discharge takes place at C2 and the charges are finally transferred to the shell M. The charges spread over uniformly on the outer surface of M raising its potential to few million volts.
We hope the Plus Two Physics Notes Chapter 2 Electric Potential and Capacitance help you. If you have any query regarding Plus Two Physics Notes Chapter 2 Electric Potential and Capacitance, drop a comment below and we will get back to you at the earliest.