Ch 8Electrostatics — Class 12 Physics, concept-first.

In Class XI you studied Gauss' law, which relates the electric flux through any closed surface to the total electric charge it encloses: where is the total electric flux coming out of a closed (Gaussi…

Gauss' law, , is exact for any closed surface, but the flux integral on the left is only easy to evaluate by hand when the chosen Gaussian surface matches the SYMMETRY of the charge distribution being…

Consider a hollow spherical shell of radius , centred at O, carrying charge spread uniformly over its surface with surface charge density (units C/m), so the total charge on the shell is .

Consider an infinitely long, thin, uniformly charged straight wire (idealised as a line), carrying a constant linear charge density (charge per unit length, units C/m), immersed in a medium of permitt…

Consider an infinite, thin, flat plane sheet carrying a uniform surface charge density (units C/m). Let P be a field point at perpendicular distance from the sheet on one side.

Just as a raised mass has gravitational potential energy that depends on its position, a charge has ELECTROSTATIC potential energy that depends on its position relative to other charges -- the stored…

Having defined potential in general, this section derives its explicit formula for three progressively richer source configurations: a single point charge (section 8.4.1), an electric dipole (section…

Let a point charge sit at the origin O, and let A be a field point at distance from it. To find the potential at A -- by definition, the work needed to bring a unit positive test charge from infinity…

Place the origin at the centre O of an electric dipole: charge at point A and at point B, separated by , with dipole moment pointing from to .

Now generalise from one or two source charges to N arbitrary point charges , sitting at respective distances from a common field point P.

An EQUIPOTENTIAL SURFACE is a surface on which the electric potential has the identical value at every single point.

The idea of potential energy from section 8.3, for just two charges, generalises directly to any number of charges by thinking OPERATIONALLY about how a system of charges is physically ASSEMBLED: imag…

Bring the first charge in from infinity to its final position . Since the second charge is still out at infinity at this stage, there is no field yet to do work against, so this first step costs zero…

Extend the two-charge result of section 8.6.1 to an arbitrary system of N point charges by continuing to bring each new charge in from infinity, one at a time, and tracking the work done against ALL t…

Up to this point, the "system" under discussion has always consisted entirely of the charges whose own mutual potential energy was being computed.

Now place TWO charges (at ) and (at ) together inside the same external field , and find the total potential energy of this combined system.

Place a complete electric dipole -- charges and separated by , dipole moment -- inside a UNIFORM external field .

A familiar everyday observation motivates this section: touching a bare wire in wet conditions, or the metal door handle of a car, can produce a mild but noticeable electric shock, while touching a pi…

A CONDUCTOR is any material containing a large population of FREE charge carriers -- in an ordinary metal, these are the valence (outermost-shell) electrons, which are only loosely bound to their pare…

Going one level deeper than the conductor/insulator distinction itself: in a metallic conductor, the electrons occupying the OUTERMOST electron shells of each atom are only loosely bound to their pare…

DIELECTRICS are insulating materials -- familiar examples include glass, wax, water, wood, mica, rubber, stone and plastic -- that can be used to STORE electrical energy, precisely because when placed…

Class XI covered the RESISTOR: a component that allows current to pass through it, but which only ever DISSIPATES the associated electrical energy as heat, with no capacity to store it.

Capacitors are said to be connected in SERIES when they are wired end to end -- the second plate of the first capacitor joined directly to the first plate of the second, and so on down the chain -- su…

Capacitors are said to be connected in PARALLEL when all of their first plates are joined together to one single common terminal A (connected onward to the applied source), and all of their second pla…

The standard PARALLEL PLATE capacitor consists of two thin conducting plates, each of area A, held parallel to one another at a suitable separation d apart, with one plate isolated and given a charge…

Start with the bare parallel-plate arrangement, no dielectric present: when charge is placed on the isolated plate, an equal and opposite is induced on the INNER face of the earthed plate (facing the…

Now insert a dielectric slab of thickness t (with , so it fills only PART of the gap, in general) between the two plates.

Ordinary direct current in a DC circuit is understood as a genuine flow of free electrons through the conducting material.

CHARGING a capacitor physically means transferring electrons from one of its plates to the other. Doing so requires the charging battery to do WORK against opposing Coulombic forces at every stage: el…

The VAN DE GRAAFF GENERATOR, designed by Van de Graaff in 1931, is a device engineered to build up extremely high electrostatic potentials -- of the order of volts -- whose resulting very large electr…

Sample papers and previous-year board questions for this subject.