Electrostatics Concept Page - 3

Example

Gold leaf electroscope

Gold leaf electroscope has two gold leafs suspended from a metal(usually brass) stem in a vacuumed glass jar and connected to a metal cap.  The glass is grounded with the help of a metal foil to make it uncharged. It can be used to:

1. Detect charge: Body under test is touched with the metal cap. If the leaves diverge, the body is charged and if there is no effect on leaves, then the body is uncharged.
2. To identify the nature of charge: The electroscope is charged by a known body(say positively charged body) and then the body is removed. Next, the body under test is brought in contact with the metal cap. If the leaves diverge further, the body has same charge(positive) and if the leaves come closer to each other, the body has opposite charge(negative).
3. Identify a body as conductor or insulator: Take two electroscopes. Charge one of the electroscopes so that its leaves will diverge. Then, connect the two electroscopes by the object under test. If the leaves of other electroscope diverge, the body is a conductor and if there is no effect on the electroscopes, the body is an insulator.

Definition

Charging by Conduction

Charging by conduction involves the contact of a charged object to a neutral object. Hence when an uncharged conductor is brought in contact with a charged conductor, charge is shared between the two conductors and hence the uncharged conductor gets charged. 
During charging by conduction, both objects acquire the same type of charge.

Definition

Charging by Induction

In this process, a charged object is brought near but not touched to a neutral conducting object. The presence of a charged object near a neutral conductor will induce (force) electrons within the conductor to move.  
The movement of electrons leaves an imbalance of charge on opposite sides of the neutral conductor. While the overall object is neutral (i.e., has the same number of electrons as protons), there is an excess of positive charge on one side of the object and an excess of negative charge on the opposite side of the object.

Result

Conduction v/s Induction

S.No	Charging by Conduction	Charging by Induction
1	Charging is done by making contact between the two bodies.	Charging is done by keeping the bodies close without touching.
2	Charge on each body changes. Total charge remains the same.	Charge on each body and the total charge remains the same.
3	When contact is removed, the charged body retains its charge.	When charged body is removed, the uncharged body again becomes neutral.

Definition

Electrostatic Induction

When an uncharged object is placed very close to a charged conductor without touching, the nearer end acquires a charge opposite to the charge on the charged conductors and the two bodies attract. This is called charging by induction. The net charge on the bodies remains the same and body is charged until they are kept close or brought in contact.   

Example

Charging by friction

By using the method of friction, positive charge is developed on one of the bodies and negative charge on the other. When these two bodies are brought close, they attract.
Some objects have tendency to gain positive charge (example glass and ebonite rod) while some objects have the tendency to gain negative charge(example silk).

Definition

Charging By Friction

When an object is rubbed with another object, the atoms in the objects get rubbed and a transfer of electrons takes place between the atoms of the two objects. One object loses electrons, while the other gains electrons. Thus, the gain of electrons or loss of electrons makes both the objects charged.  

Law

Coulomb's Law

Coulomb measured the force between two point charges and found that it varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges. Thus, if two point charges q1, q2 are separated by a distance r in vacuum, the magnitude of the force (F) between them is given by
F=k|q1q2|r2$F=k{\displaystyle \frac{|q_1{q}_2|}{r^2}}$

Definition

Value of constant in Coulomb's Law and permittivity of free space

k=14πϵ0$k={\displaystyle \frac{1}{4\pi {ϵ}_0}}$
In SI units, the value of k is about 9×109N.m2/C2$9\times {10}^{9}N.m^2/C^2$.
where ϵ0${ϵ}_0$ is called the permittivity of free space . The value of ϵ0${ϵ}_0$ in SI units is ϵ0=8.854×10−12C2N1m2${ϵ}_0=8.854\times {10}^{-12}{C}^2{N}^1{m}^2$.

Definition

Comparison of coulomb's law and newton's law of gravitation

According to coulomb's law, force between two charged particles is given by:
F=Q1Q24πεoR2$F={\displaystyle \frac{Q_1{Q}_2}{4\pi {\epsilon }_o{R}^2}}$
According to newton's law of gravitation, force between two charged particles is given by:
F=GM1M2R2$F={\displaystyle \frac{G{M}_1{M}_2}{R^2}}$
The similarities in the formula of force in the two laws is evident. There are two differences between them though:
1. Coulomb's force may be attractive or repulsive depending on the nature of charges involved which gravitational force is always attractive.
2. Coulomb's force depends on the medium between the charges which is false for the gravitational force.
Coulomb's law is very useful and gives verification of the presence of electrons in an atom.

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