Ch 1Electrostatics — Class 12 Physics, concept-first.

In Class XI, we studied several everyday forces -- gravitational force, tension, friction, and the normal force -- treating each of them, as Newton did, as though they were independent, unrelated forc…

Two millennia ago the Greeks noticed that amber (fossilised tree resin), after being rubbed with animal fur, would attract small bits of leaves and dust; the amber was said to have become 'charged'.

Three basic properties define electric charge. (i) Electric charge: like mass, electric charge is an intrinsic property of the fundamental particles that make up matter -- protons carry charge +e and…

In 1785, Charles-Augustin de Coulomb deduced the expression for the force between two stationary point charges q1 and q2 separated by a distance r in vacuum.

Coulomb's law by itself only describes the interaction between exactly two point charges; when more than two charges are present, Coulomb's law alone cannot say what net force one particular charge ex…

Coulomb's law describes the force between two charges but does not explain how that interaction is actually transmitted through empty space between them -- historically this puzzle was called 'action…

To describe how a source charge q influences the space around it, physicists define a quantity called the electric field intensity, or simply the electric field E, at every point in that space.

When a number of point charges are distributed through space, the electric field they jointly produce at some field point P is found using the same superposition principle used earlier for forces.

Although electric charge is fundamentally quantised at the microscopic (atomic) level, most everyday charged objects -- a charged rod, ring, disc, or sphere -- contain such an enormous number of eleme…

An electric field line is an imaginary curve, introduced by Faraday, drawn so that the tangent to the curve at any point gives the direction of the electric field at that point.

Two equal and opposite charges (+q and -q) separated by a small distance constitute an electric dipole.

Two equal and opposite charges +q and -q, separated by a small distance 2a, together constitute an electric dipole.

The electric dipole itself produces an electric field in the surrounding space, obtained by superposing the individual point-charge fields of its +q and -q charges.

Consider a dipole of moment p placed inside a uniform external electric field E, whose field lines are parallel and equally spaced everywhere.

In mechanics, potential energy is defined only for conservative forces, such as gravity, whose gravitational potential energy was introduced in Class 11 (Unit 6).

Consider a positive charge q kept fixed at the origin, producing an electric field in the surrounding space.

For an isolated point charge q kept fixed at the origin, the electric potential at a point P a distance r away is found by computing the work per unit charge required to bring a positive test charge i…

Consider a dipole with charges +q and -q separated by a small distance 2a, and a field point P located a distance r from the dipole's midpoint O, where the line OP makes an angle theta with the dipole…

A surface on which the electric potential has the same value at every point is called an equipotential surface.

Consider a positive charge q fixed at the origin, and a unit positive test charge moved a small distance dx toward q, in the same direction as the electric field E produced by q.

The electric potential at a distance r from a point charge q1 is V = k q1/r. If a second charge q2 is now brought in from infinity to a point a distance r12 from q1, the work needed to do so is W = q2…

When a dipole of moment p is placed in a uniform electric field E, it experiences a torque tau = pE sin(theta) tending to rotate it toward alignment with the field (section 1.4.3); rotating the dipole…

This section builds, in stages, one of the most powerful tools in electrostatics. It starts from the simple geometric idea of electric flux -- essentially a count of how many field lines pass through…

The number of electric field lines crossing a given area, held perpendicular to the field, is called the electric flux through that area, usually denoted PhiE.

The idea of flux, developed in section 1.6.1 for an open (flat or curved but not fully enclosing) surface, extends naturally to a closed surface -- a surface, such as a sphere, cube, or cylinder, that…

A positive point charge Q is imagined surrounded by a sphere of radius r centred exactly on it. Because every point of the sphere's surface is the same distance r from Q, the field E has the same cons…

Although the electric field due to any given charge configuration can, in principle, always be computed either by direct application of Coulomb's law (using the superposition and integration technique…

Materials fall into two broad classes for the purposes of electrostatics. Conductors, such as metals, contain a large number of charges (in metals, free electrons not bound to any particular atom) tha…

A conductor contains a very large number of mobile charges -- in a metal, free electrons not bound to any particular atom -- that are free to move throughout the material.

One of the most useful practical consequences of a conductor's electrostatic properties concerns a hollow conductor -- a conductor with an empty cavity carved out of its interior.

Electrostatic induction is the process by which a conductor becomes charged through the mere proximity of a charged object, without the two ever touching.

A dielectric is a non-conducting material with no free electrons -- every electron in a dielectric remains bound within its own atom or molecule. Ebonite, glass and mica are common examples.

When an external electric field Eo is applied to a dielectric, whether by inducing new dipoles in a non-polar dielectric or by aligning the pre-existing dipoles of a polar one, the resulting polarised…

When the external electric field applied to a dielectric becomes very large, it can tear the bound electrons away from their parent atoms, converting the previously bound (immobile) charges into free…

A capacitor is a device used to store electric charge and, along with it, electrostatic potential energy.

The most common and simplest capacitor geometry is the parallel-plate capacitor: two identical flat conducting plates, each of area A, held parallel to each other and separated by a small distance d,…

A capacitor stores not only charge but also electrical energy. As a battery charges a capacitor, it transfers charge from one plate to the other in a series of small increments; at the moment when a c…

Because a capacitor can be charged relatively slowly and then discharged very rapidly, releasing its entire stored energy in a short burst, capacitors are used throughout electronics wherever a sudden…

When a dielectric of relative permittivity epsilonr is introduced to fill the space between an already-charged parallel-plate capacitor's plates, the outcome depends on whether the battery is left con…

(i) Capacitors in series: consider capacitors C1, C2 and C3 connected end to end in a single chain (series) across a battery of voltage V.

The unit's final section brings together several earlier results -- that a conductor's whole surface sits at one uniform potential, that a conductor's free charge resides entirely on its surface, and…

Consider two conducting spheres A and B, of radii r1 and r2, connected to each other by a long thin conducting wire, with the separation between the spheres taken to be much larger than either radius.…

Because the surface charge density on an irregularly shaped charged conductor is greatest at its most sharply curved regions (as shown in section 1.9.1), and the field just outside any charged conduct…

A lightning arrester, also called a lightning conductor, is a device used to protect tall buildings from lightning strikes, and it works directly on the principle of action at points (corona discharge…

In 1929, the American physicist Robert Van de Graaff designed a machine, now called the Van de Graaff generator, capable of building up an extremely large electrostatic potential difference, of the or…

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