Electrostatics I

Coulomb's Laws in Electrostatics
Electric Field
Motion of a Charged Particle in an Uniform Electric Field
Electric Lines Of Forces

Electric Charge





Charge is the property associated with matter due to which it produces and experiences electrical and magnetic effects.

The SI unit of charge is coulomb, denoted by C.

Properties Of Charge







(1) Charge is always associated with mass.
(2) Charge is quantised.
(3) Charge is conserved.
(4) Charge is invariant.




Conductors And Insulators



The conductors are materials, which allow electricity (electric charge) to pass through them due to the presence of free electrons.
Materials such as tap water, human body, earth, damp wood, electrolytes (solutions of salts, acids or alkalies in water) and metals such as copper, gold, aluminium, etc., are good conductors.

The insulators are the materails, which do not allow (electric charge) to pass through them as there is no free electrons in them.
Non-metals like rubber, plastic, silk, wool, ebonite, mica, glass, chemically pure water, etc. are the examples of insulators.
Top

Coulomb's Law

" Two stationary point charges repel or attract each other with a force which is directly proportional to the product of the magnitudes of their charges and inversly proportional to the square of the distance between them."











where K is the Constant of Proportionality. The value of K depends upon the medium in which two point charges are placed.
In S.I. system,

Coulomb's law in Vector form


Let us consider two points charges q1 and q2 separated by a distance d. Charge q1 exerts force on charge q2 and also the charge q2 exerts force on q1. The direction of the force depends upon the nature of charges. Now, if q1q2 > 0 , i.e. both and are positive or negative, will repel each other. On the other hand if q1q2 < 0 , i.e. both charges are unlike or dissimilar, then charges attract each other.





























Top

Principle of Superposition

Superposition principle states that the electric force experienced by a charge due to other charges is the vector sum of the individual electric forces acting on it due to all other charges. Superposition principle enables us to obtain the total force on a given charge due to any number of point charges. The main idea behind this principle is that the field due to any charge is independent of the presence or absence of all other charges.
Consider a system of charges consisting of n charges q1, q2, q3, ... . Charge q1 will experience force due to charges q2, q3, ... . Similarly charge q2 will experience force due to charge q1, q3, ... and so on other charges. The net electric force acting on charge q1 will be the resultant of all the forces acting on it due to presence of charges q2, q3, ...



Electric Field

The electric field is defined as the force per unit charge exerted on a small positive test charge (q0) placed at that point. Mathematically,





An electric field may also be defined as a region in which there should be a force on a charge brought into that region. Whenever a chrge is placed in an electric field, it experiences a force.
Electric fields are usually produced by different types of charged bodies - point charges, charged plates, charged sphere etc.














Electric Field of Point Charge


The electric field of a point charge can be obtained from Coulomb's law:














The electric field is radially outward from the point charge in all directions. The circles represent spherical equipotential surfaces.

The electric field from any number of point charges can be obtained from a vector sum of the individual fields. A positive number is taken to be an outward field; the field of a negative charge is toward it.



Motion of a Charged Particle in an Uniform Electric Field

Top

Electric Lines of Force


A more generalized way of representing an electric field produced by a source is, other than representing it by arrows, in terms of Electric Lines of Force [first put forth by Michael Faraday (1791–1867)].

It is the path along which a unit positive charge would move when kept in an electrostatic field.

In other words, a field line is an imaginary line drawn in such a manner that its direction at any point is the same as the direction of the field at that point. A line of force is the curve drawn in electric field whose tangent at any point gives the direction of intensity at that point.

PQ is an electric line of force. The tangent to the line PQ at point A gives the direction of electric intensity at A. Similarly, the tangent to the line PQ at B gives the direction of intensity at B.



Certain cases of Electric lines of forces



The lines of forces due to a single positive point charge are shown . As positive charge will repel positive test charge so direction of electric field lines are away from positive charge.




The lines of forces due to a single negative point charge are shown below. As negative charge will repel positive test charge so direction of electric field lines are towards the negative charge.




Lines of forces due to a pair of equal and opposite charges are shown below.











Lines of forces due to two equal positive charges are shown below.













Lines of forces due to two unequal positive charges are shown below.












Well it can be seen that when the charges are equal, point M lies at the centre of the line joining the charges. On the other hand when the charges are unequal, the neutral point M is closer to the smaller charge.



Properties of Electric Lines of Force



>> The electric lines of force are imaginary lines depicting the partial qualitative information about the field.

>> Two lines of force always repel each other laterally.

>> Two lines of force will never intersect each other, because if it happens, there will be two directions of intensity at that point of intersection which is not feasible.It can be seen in the figure given below that if two lines intersect at point M. Then there are two directions of electric field at a point M given by two tangents MP and MQ, which is not possible.

>> Electric lines of forces are always normal to the surface, both while starting and ending. Thus, there is no component of electric field parallel to the surface of the conductor.

>> Tangent to the line of force at any point gives the direction of the electric intensity that point.

>> In case of a positively charged body, the electric lines of force are directed away from the body. If the body is negatively charged, then the lines of force are directed towards the body.
Top
Clicky Web Analytics