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Electrostatics is an important topic from JEE Main / JEE Advanced Exam Point of view. Every year
there are 1-3 questions asked from this topic. This short notes on Electrostatics will help you in revising
the topic before the JEE Main & IIT JEE Advanced Exam.
Electric Potential and Capacitance
Electric Potential Energy- It is defined as the work done in moving a charge from one point to the
other.
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Electric Potential- It is defined as the change in the Electric potential energy per unit charge.
Electric potential due to a point charge- The Electric potential due to a point charge at any distance r
is
Electric potential due to a system of charges- For a discrete system of charges the electric potential
will use the same principle of superposition. The net potential due to the system of charges is equal to
the sum of the sum of the individual potentials.
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Electric potential due to an Electric Dipole- Potential due to electric dipole depends on r and on the
angle between position vector and dipole moment.
The Potential at any point form the centre of the dipole is
Equipotential Surface- If the charge is uniformly distributed over the surface then the potential at each
and every point is same then that surface is considered as an Equipotential Surface.
So the work done to move a charge from one place to other on an equipotential surface is zero.
Potential energy of a system of two-point charge- The energy that result from the collection of
charges when the charge will employ a force on any other charge. It is the total amount of work done in
moving the charges from an infinite distance to their corresponding positions in the system.
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is the position vector between the charges .
Potential energy of electric dipole in an electric field
As the electric field implies torque in the dipole, the work done in rotating it against the torque is stored
in the form of its potential energy.
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Conductor, Insulator and Dielectric
Conductors and Insulators- The materials that allow the free movement if electrons or charge carriers
are known as Conductors and the material that avoid any sort of flow of the charged carriers is known
as Inductors.
Points to remember
1. The electrostatic field inside an inductor is zero.
2. At the surface of a charged conductor at every point, the electrostatic field is normal to the surface.
3. In the static situation, the interior of a conductor has no excess charge.
4. At the surface of the charged conductor electric field is
5. The electrostatic field inside a metal cavity is always zero.
Free Charges- Free charges that move throughout the conductor without any constraint. E.g. Electron
or ion moving inside a vacuum.
Bound Charges- Bound charge cannot move in response to an external electromagnetic. E.g. Atoms in
an insulator undergoes charge separation when subjected to an electric field, resulting in the formation
of dipoles that align themselves to counteract the subjected field.
Dielectric Materials- Dielectric materials are non-conducting substances where the free movement of
charges is not possible. The external field induces a dipole moment by re-orienting molecules of the
dielectric which in return produces a field that opposes the external field.
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Polarisation- Polarization is a phenomenon occurs when an external electric field alters the negative
cloud of electrons around positive atomic nuclei in the opposite direction of the applied field. This
insignificant separation of charge makes one side of the atom slightly positive and the opposite side
somewhat negative.
Thus, Polarization is a comparative shift of positive and negative in opposite directions inside an
insulator or dielectric stimulated by an external field.
Polarisation is expressed as , where is the constant of dielectric and known as
Electrical susceptibility, and is the applied Electric field.
The Electrical susceptibility is also defined the degree of allowance for electric field lines to penetrate
into the dielectric.
It can also be expressed in terms relative permittivity .
Capacitor and Capacitance
Capacitor- Capacitor is a two-terminal electrical passive component that used to store the energy in the
electrical field.
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Capacitance (C) - Capacitance is the ability of a capacitor to store electrical energy is known as its
Capacitance.
, where Q is the charge, and V is the voltage.
The constant C is called the capacitance of the capacitor. It is independent of charge or potential and
depends only on the geometrical alignment of the system of two conductors.
Parallel Plate Capacitor: It consists of two large plane parallel conducting plates separated by a small
distance and charge is distributed along the conducting surface of the plates.
The capacitance of a parallel plate capacitor is
Combination of Capacitors
Series Combination- If two capacitor C1 and C2 are connected in series then the net capacitance
is
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If n capacitors are connected in series, then the net capacitance is
Parallel combination- If two capacitor C1 and C2 are connected in parallel then the net capacitance
is
If n capacitor are connected in parallel then the net capacitance is
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Effect of dielectric on capacitance- If a dielectric medium of dielectric constant k is inserted between
the plates of the capacitor then the net capacitance of the capacitor is,
where is the dielectric constant of the material, Co is the capacitance without the dielectric.
Energy stored inside the capacitor- In a capacitor, the work done on moving a positive charge from a
negative conductor to a positive conductor against the repulsive forces is stored as energy stored in the
plates of the Capacitor.
, where Q is the charge, C is the capacitance of the capacitor.
Van De Graf Generator
Van De Graf Generator is an electrostatic generator that is capable of generating a large static electric
potential. It creates a very high electric potential in the order of a few million volts which results in a
very large electric field at least until breakdown field of air is reached.
It uses a moving belt that stores charge on a hollow metal structure. The hollow metal structure has a
design of a globe which is placed on the top of a column that is insulating in nature.
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Working- A large spherical shell is placed at some height above the ground. An insulating column is
fixed which holds it. Two pulleys are coiled with a belt-like insulating material, with one being at
ground level and the other one at the centre of the shell. The belt carries out a nonstop motion, thus
carrying a positive charge constantly from the ground to the top. This belt is kept moving continuously
by a motor driving the lower pulley. The positive charge is transferred to the larger shell by a carbon
brush, thus coating the outer shell with a very high potential over the time.
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