Notes for Electrostatics chapter of class 12 physics. Dronstudy provides free comprehensive chapterwise class 12 physics notes with proper images & diagram.

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** Charge **is the property of

There exist two types of charges in nature : ** positive **and

The type of charge on an electron is negative. The charge of a proton is the same as that of an electron but with a positive sign. In an atom, the number of electrons and the number of protons are equal. The atom is, therefore, electrically neutral. If one or more electrons are added to it, it becomes negatively charged and is designated as negative ion. However, if one or more electrons are removed from an atom, it becomes positively charged and is called a positive ion.

The *excess *or* deficiency* of electrons in a body gives the concept of charge. If there is an excess of electrons in a body, it is negatively charged. And if there is deficiency of electrons, the body becomes positively charged. Whenever addition or removal of electrons takes places, the body acquires a charge.

The **SI Unit** of charge is **coulomb **(**C**). In SI units, the current is a fundamental quantity, having a unit of ampere (A). The unit of charge is defined in terms of the unit of current. Thus, *one coulomb is the charge transferred in one second across the section of a wire carrying a current of one ampere*.

Â Â Â Â Â As Â Â Â *q* = *It*, we have

1 C = (1 A) (1 s)

Â Â Â Â Â The dimensions of charge are [A T].

**(1)**Â ** Quantization of Charge **:Â Electric charge can have only discrete values, rather than any value. That is, charge is

*e* =Â Â± 1.6 x 10^{-}^{ 19} C

This is the charge attained by an electron and a proton.

A charge *q* must be an integral multiple of this basic unit. That is,

*Q* = Â± *neÂ Â Â Â Â Â Â Â *where *n* = 1, 2, â€¦

Charge on a body can never be (Â½)*e*, (^{2}/_{3})*e*, or 5.7*e*, etc.

When we rub a glass rod with silk, some electrons are transferred from the rod to the silk. The rod becomes positively charged. The silk becomes negatively charged. The coulomb is a very large amount of charge. A typical charge acquired by a rubbed body is 10 ^{-}^{ 8 }C.

*ApplicationÂ 1
*

*Solution:*

Given *q* = +0.32 C. Since the charge is positive, there is deficiency of electrons.

Â = 2 x 10^{18} electrons

**Note** that the electron itself is not the charge; ** charge is a property**, like mass, of elementary particles, such as the electrons, protons, etc.

**(2)Â Charge is Always Associated with Mass **: A charge cannot exist without mass, though a mass can exist without charge. The particles such as

The mass of a body (slightly) increases when it acquires a negative charge (by gaining some electrons). On the other hand, when a body acquires a positive charge (by losing some electrons), its mass (slightly) decreases.

**(3)Â Conservation of Charge **: In an

**Note **that in pair production and pair annihilation, neither mass nor energy is conserved separately, but (mass + energy) is conserved. In pair production energy is converted into mass, while in annihilation mass is converted into energy.

Conservation of charge holds good in all types of reactions.

For example :

** Chemical Reaction **:

Â Â Â Â Â Â Â Â Na^{+Â }Â Â +Â Â Â Â Cl^{-}^{Â }Â Â NaCl

Â Â Charge : Â (+*e*)Â Â + Â (-*e*)Â Â = Â (0)

** Radioactive Decay **:

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â n Â Â Â Â Â Â Â p Â Â Â Â Â Â Â Â + Â Â Â Â Â Â Â Â e^{-} Â Â Â Â Â Â Â Â Â Â Â + Â Â Â Â Â

Charge :Â Â Â Â Â Â Â Â Â (0) Â Â Â Â = Â Â Â (+*e*) Â Â Â Â + Â Â Â (-*e*) Â Â Â Â Â Â Â Â + Â Â Â Â (0)

**(4)Â Invariance of Charge **:Â Numerical value of a charge is independent of the frame of reference. It means the value of charge on a body remains the same, whether it is stationary, or moving with a constant velocity or accelerating. In contrast, the mass of a body depends on its speed, and it decreases with increase in speed.

The force of interaction of two stationary point charges in vacuum is directly proportional to the product of these charges and inversely proportional to the square of their separation,

where *F* is in newton, *q*_{1} and *q*_{2} in coulomb, *r* in metre, and *k* is a constant given in SI units by

Â = 9 x 10^{9} N m^{2} C^{-}^{2
}

where Â = 8.85 Â´ 10^{-}^{12} C^{2} N^{-}^{1} m^{-}^{2} and is called the ** permittivity of free space **(vacuum or air).

For mediums other than air or vacuum, the electrostatic force between two charges becomes

Here , is called the ** absolute permittivity** or

The ** coulomb force **acts along the straight line connecting the points of location of the charges.

This force is

The

For example, to find the force on

Â Â Â Â Â means a repulsion

whereas, Â Â Â Â Â Â Â means an attraction

Coulombâ€™s law is analogous to Newtonâ€™s law of gravitation :

However, following are the important *differences *:

(*a*)Â Electric force between charged particles is much stronger than gravitational force, i.e., *F _{E}* >>

(e.g. between two electrons

(

(

**(1)Â Charges are Assumed to be at Rest :**Â When charges are in motion they also produce and experience magnetic forces.

**(2)Â Charges are Assumed to be on Point Particles** : Coulombâ€™s law cannot be directly applied to a

The coulombâ€™s law obeys the principle of superposition. *It* *means that the force between two particles is not affected by the presence of other charges*. This principle is used to find the net force exerted on a given charged particle by other charged particles.

The force on a charged particle *q*_{1} due to point charges *q*_{2}, *q*_{3} and *q*_{4} is the resultant of forces due to individual point charges, i.e.,

**Note** that the notation represents the force on *q*_{1} due to *q*Â_{2}.

(1)Â Decide whether the force due to a given charge is *attractive *or* repulsive *and show it by drawing vector, pointing *towards* or *away from* the given charge, respectively.

(2)Â Find the magnitude of the force using Coulombâ€™s law---*ignoring the signs of the charges*.

(3)Â Resolve the forces along the given co-ordinate axes and express them in vector form using unit vector notation, unless otherwise specified.

(4)Â Use the principle of superposition to find the net force on the charge.

*Application 2
*

(2) The *magnitude *of the forces , and Â are

(3) Â

Â Â + Â

(4)Â The net force on *q*_{1} is

*Application 3
*

*Solution:*

Had there been sixth charge +*q* at the remaining vertex of hexagon, the net force due to all the six charges on â€“*q* at O would be zero. The forces due to individual chargesÂ will balance each other. That is,

Now if Â is the force due to sixth charge and due to remaining five charges, we must have

Â i.e., Â Â Â Â Â

or Â Â Â

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