1. Electric Potential
Electric potential at any point in an electric field is the work done in bringing a unit positive charge from infinity to that point, without acceleration.
- Electric Potential (V): It is a scalar quantity.
- Unit: Volt (V).
- Formula:
Electric potential V at a distance r from a point charge Q is given by:
V = k multiplied by Q divided by r,
where
k is Coulomb’s constant (9 multiplied by 10 raised to the power of 9 N m squared per C squared). - Relation with Electric Field:
The electric field is the negative gradient of electric potential, i.e.,
E = negative dv divided by dr.
2. Electric Potential Difference
The electric potential difference between two points in an electric field is defined as the work done in moving a unit positive charge from one point to the other.
- Formula:
Delta V = W divided by q,
where
W is the work done, and
q is the charge.
3. Equipotential Surfaces
Equipotential surfaces are surfaces where the electric potential is the same at every point.
Properties of Equipotential Surfaces:
- No work is required to move a charge along an equipotential surface.
- The electric field is always perpendicular to an equipotential surface.
- Equipotential surfaces never intersect.
4. Electric Potential Due to a Point Charge
The potential at a point due to a point charge Q at a distance r is given by:
- Formula:
V = k multiplied by Q divided by r,
where
k is Coulomb’s constant, Q is the charge, and r is the distance from the charge.
5. Electric Potential Due to a System of Charges
For a system of point charges, the total potential at a point is the algebraic sum of the potentials due to individual charges.
- Formula:
V = V1 plus V2 plus V3 plus …
where V1, V2, and V3 are the potentials due to individual charges.
6. Potential Energy in an External Electric Field
When a charge q is placed in an external electric field E, it experiences a force. The potential energy (U) of the charge in the electric field is the energy possessed by the charge due to its position.
- Formula:
U = q multiplied by V,
where V is the potential at that point.
7. Capacitance
Capacitance is the ability of a system to store electric charge. It is defined as the ratio of the charge stored on the plates of a capacitor to the potential difference between them.
- Formula:
C = Q divided by V,
where
C is the capacitance,
Q is the charge stored, and
V is the potential difference. - Unit: Farad (F).
8. Parallel Plate Capacitor
A parallel plate capacitor consists of two parallel conducting plates separated by a distance. The capacitance of a parallel plate capacitor depends on:
- Area (A) of the plates,
- Distance (d) between the plates,
- Permittivity (epsilon) of the material between the plates.
- Formula:
C = epsilon naught multiplied by A divided by d,
where
epsilon naught is the permittivity of free space.
9. Capacitance with a Dielectric
When a dielectric material of dielectric constant K is inserted between the plates of a capacitor, the capacitance increases by a factor of K.
- Formula:
C = K multiplied by C0,
where C0 is the capacitance without the dielectric.
10. Energy Stored in a Capacitor
The energy stored in a charged capacitor is the work done in charging the capacitor.
- Formula:
U = 1 divided by 2 multiplied by C multiplied by V squared,
where
U is the energy stored,
C is the capacitance, and
V is the potential difference.
11. Combination of Capacitors
Capacitors can be combined in two ways:
- Series Combination:
In series, the reciprocal of the total capacitance is equal to the sum of the reciprocals of the individual capacitances.
- Formula:
1 divided by C total = 1 divided by C1 plus 1 divided by C2 plus 1 divided by C3.
- Parallel Combination:
In parallel, the total capacitance is the sum of the individual capacitances.
- Formula:
C total = C1 plus C2 plus C3.
12. Van de Graaff Generator
The Van de Graaff generator is a device used to produce very high voltages by transferring charge to a large spherical conductor.
Working Principle:
- Charges are transferred to a conducting belt which then transfers the charge to the large spherical dome.
- The potential difference created can be extremely high, useful in particle accelerators and electrostatic experiments.
13. Important Questions for Practice
- Define electric potential and potential difference.
- Derive the expression for the capacitance of a parallel plate capacitor.
- What is an equipotential surface? State its properties.
- Explain the effect of a dielectric on the capacitance of a capacitor.
- Derive the energy stored in a capacitor.
- What is the working principle of the Van de Graaff generator?
