Electrostatic Potential and Capacitance Summary

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Potential Energy

• : is the work done at a point by an external agent in moving a unit positive charge from infinity to a given point against the electrostatic field.

Potential due to a point charge 'q'

If q > 0, V is positive and if q < 0 potential is negative.

Potential due to a number of charges

• Equipotential surface is the locus of points at which the potential due to a charge distribution is the same.

• Electric lines of forces and equipotential surface constitutes a mutual perpendicular network.

Potential energy stored in a system of charges

where r₁₂ is the distance between charges q₁ and q₂.

• The electric field at a point is equal to the negative gradient of the electric potential. Negative sign indicates that the direction of electric field is always in the direction of decrease of electric potential.

SI unit = Vm^-1

Potential energy of a dipole in a uniform electric field E

V = -p . E

where 'p' is dipole moment

Conductors and their properties

• Conductors have free electrons.

• Electrostatic field inside a conductor is zero.

• At the surface, electrostatic field is normal to the surface at every point.

• Electrostatic field at the surface of charged conductor is given by

• Electrostatic shielding

• Capacitance C = q/v, where 'q' is charge on the conductor and 'v' the potential difference between the two conductors.

• Unit of capacitance is Farad.

• Polarisation is the effect produced when a dielectric is placed between two plates of a capacitor. The electric field due to the charged plates induces a net dipole moment in the dielectric.

• Van De Graff Generator is also known as belt generator. It is an electrostatic machine which was designed in 1931 by Van De Graff to generate energy. Initially it generated 1.5 MeV. Later on went on generate 20 MeV. This generator is used to accelerate negative charges.