Physics capacitors

1. ❑ Phenomenon of
polarization of charges
in a body, when a
charged body is present
near it, is called
electrostatic induction.
❑ In this process bodies
are charged without
touching them.
ELECTROSTATIC INDUCTION

2. CHARGING BY INDUCTION

3. ❑ A charged object will induce a charge on a nearby
conductor. In this example, a negatively charged rod
pushes some of the negatively charged electrons to the
far side of a nearby copper sphere because like charges
repel each other.
❑ The positive charges that remain on the near side of the
sphere are attracted to the rod.
❑ If the sphere is grounded so that the electrons can
escape altogether, the charge on the sphere will remain
if the rod is removed.

4. CAPACITOR AND CAPACITANCE
A capacitor is a two-terminal electrical device that
can store energy in the form of an electric charge.
It consists of two electrical conductors that are
separated by a distance.
The space between the conductors may be filled by
vacuum or with an insulating material known as a
dielectric.
The ability of the capacitor to store charges is known
as capacitance.

5.  Capacitance of a conductor is defined as the
charge required to raise its potential through
one unit.
SI Unit of capacitance is ‘farad’ (F).
Symbol of capacitance:

6. Behavior of Conductors in the
Electrostatic Field:
1.Net electric field intensity in the interior of a
conductor is zero.
2.Electric field just outside the charged conductor is
perpendicular to the surface of the conductor.
3.Net charge in the interior of a conductor is zero.
The charges are temporarily separated. The total
charge of the system is zero.

7. 4. Charge always resides on the surface of a conductor
 Electric potential is constant for the entire
conductor.
 Surface charge distribution may be different at
different po
 int

8.  Generally, a non-conducting medium or insulator is
called a ‘dielectric’.
 Precisely, the non-conducting materials in which
induced charges are produced on their faces on the
application of electric fields are called dielectrics.
 E.g. Air, H2, glass, mica, paraffin wax, transformer
oil, etc.
Dielectrics:

9. Polarization of Dielectrics
 When a non-polar dielectric slab is subjected to an
electric field, dipoles are induced due to separation
of effective positive and negative centers.
 E0 is the applied field and Ep is the induced field in
the dielectric.
 The net field is EN = E0 – Ep
 i.e. the field is reduced when a dielectric slab is
introduced. The dielectric constant is given by

10. Polarization Vector
 The polarization vector measures the degree of
polarization of the dielectric.
 It is defined as the dipole moment of the unit volume
of the polarized dielectric.
 If n is the number of atoms or molecules per unit
volume of the dielectric, then polarization vector is
 SI unit of polarization vector is C m-2.

11. Dielectric Strength:
Dielectric strength is the maximum value
of the electric field intensity that can be
applied to the dielectric without its
electric break down.
Its SI unit is V m-1.

12. Capacitance of Parallel Plate Capacitor:
 Parallel plate capacitor is an arrangement of two
parallel conducting plates of equal area separated
by air medium or any other insulating
medium such as paper, mica, glass, wood, ceramic,
etc….

13. If the space between the
plates is filled with
dielectric medium of relative
permittivity εr, then
Capacitance of a parallel
plate capacitor is
(i) directly proportional to the area of the plates and
(ii) inversely proportional to the distance of separation
between them

14. Series Combination of Capacitors:
In series combination,
i) Charge is same in each capacitor
ii) Potential is distributed in inverse proportion to
capacitances

16. The reciprocal of the effective capacitance is the
sum of the reciprocals of the individual capacitances.
Note: The effective capacitance in series combination is
less than the least of all the individual capacitances.

17. Parallel Combination of Capacitors:
In Parallel connection

19. Capacitance of Parallel Plate Capacitor with
Dielectric Slab:
•The charge on a parallel plate capacitor – q
•Area of slab – A
•The distance between the parallel plate – d
•The dielectric constant of the slab of a material – K
•The thickness of the material –t
•The vacuum between the plates – (d-t)
•The surface charge density on the plates – 

20. V = E0 (d – t) + E t
The electric field in the air between the
plates is E0 = =
The electric field in the dielectric material
E =
The potential difference between the plates
Now substitute the values of E0 & E in the
above equation

21. Since K>1, the effective distance between
the plates becomes less than d and so the
capacitance increases.

22. Application of Capacitors
1. Flash Capacitors used in digital cameras for taking
photographs.
2. It is used in defibrillator.
3. It is used in automobile engines.
4. It is used to reduce power fluctuations in power
supplies.
5. It is used in energy storage.
6. RF Coupling and Decoupling.

23. The process of charging a capacitor is
equivalent to transferring charges from one plate to
the other of the capacitor.
The moment charging starts, there is a potential
difference between the plates. Therefore, to transfer
charges against the potential difference some work is
to be done. This work is stored as electrostatic
potential energy in the capacitor.
If dq be the charge transferred against the
potential difference V, then work done is
Energy Stored in a Capacitor:

25. • SI unit of energy density is J m-3.
Energy Density
• Energy density is generalized as energy per
unit volume of the field.

26. Energy Stored in a Series Combination of Capacitors
Energy Stored in a Parallel Combination of Capacitors