ELECTROSTATICS FOR CLASS XII


Electrostatics deals with the study of electric charges at rest.

When certain substances are rubbed with other suitable substances, they acquire the property of attracting small pieces of straw, feather etc, towards it. Eg: A glass rod rubbed with silk, an ebonite rod rubbed with fur etc. The attractive property is due to the presence of electric charges on them. The glass rod and the ebonite rod are said to be electrified or electrically charged.

When a glass rod rubbed with silk is brought near another glass rod similarly rubbed with silk, the two rods are found to repel each other. Hence there must be a force of repulsion between the charges developed on the two rods. But if an ebonite rod rubbed with fur is brought near a glass rod rubbed with silk, the two rods attract each other. So there must be a force of attraction between the charges on the two rods. From these experiments it is clear that there are two kinds of electric charges. The charge acquired by the glass rod rubbed with silk is called positive electric charge and that acquired by the ebonite rod rubbed with fur is called negative electric charge. The above experiments show that like charges repel and unlike charges attract each other.

Conductors, Insulators and Semiconductors

Substances which allow electric charges to flow through them are called conductors. Eg. All metals, Carbon etc.

Substances which are not allowed electric charges to flow through them are called insulators. Eg. Paper, leather, wood, glass, ebonite, wax etc.

Substances which have an electrical conductivity intermediate between those of conductors and insulators are called semiconductors. Eg. Germanium, Silicon, Selenium, Silver Sulphide etc.

Electrostatic Induction

It is possible to charge a conductor by bringing a charged body near it. When a positively charged body A is brought near a conductor BC, negative charges appear at the near end B and positive charges at the farther end C. Thus unlike charges are induced at the near end and like charges at the farther end of the conductor. This process is called electrostatic induction or electrification by induction. The charge on the body A is called the inducing charge and the charges appearing on BC are called inducted charges. The induced charges (each type) will be equal in magnitude to the inducing charge. When the body A is removed, the charges on BC will disappear. This shows that the induced charges will exist only as long as the inducing charge is present.

Coulomb’s Law (Inverse Square Law) of electrostatic force

The force of attraction or repulsion between two stationary charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let r be the distance between two stationary charges q1 and q2 in free space. Then the force of attraction or repulsion between them can be given by

F α q1q2 and F α r2

Ie. F α q1q2/r2

Or F = K q1q2/r2

Electric Field

The region around any electric charge where its effects (attractive force or repulsive force) can be experienced is called the electric field of the charge. The electric fields produced by a stationary electric charges is called an electrostatic field.

Intensity of Electric Field (E)

The intensity of electric field (or electric field strength) at a point in an electric field is the force exerted on a unit positive charge placed at that point.

Ie E = F/q

Therefore the Unit of E = Unit of Force/Unit of q
= Newton/Coulomb (N/C)

It may be shown that Volt per metre is also the unit for electric field.

Dimensions of E = Dimensions of Force/Dimensions of Charge
= MLT-2/IT
=M1L1I-1T-3

Lines of Force

An electric filed may be represented by a number of imaginary lines of force. A line of force may be defined as a smooth, continuous curve along which unit positive charges free to move would move. The tangent at any point on the curve gives the direction of the electric field at that point.

Properties

1) Since the intensity of the field due to a positive charge is directed away from it, the lines of force proceed from the positive charge. Since the intensity of the field due to a negative charge is directed towards it, the lines of force proceed towards the negative charge and end at it. Thus lines of force start from positive charges and go to infinity or end at negative charges.
2) The number of lines of force passing through unit area taken around a point perpendicular to the direction of the electric filed gives the magnitude of the field at the point.
3) The direction of the tangent drawn to the line of force at any point gives the direction of the electric field at that point.
4) Only one line of force can pass through a given point, since the intensity of the electric field has a unique direction at each point. Thus two lines of force can never intersect.

Lines of force in a uniform electric filed are parallel, equidistant and in the same direction. Lines of force due to an isolated positive charge, an isolated negative charge, two positive charges, and due to a positive and a negative charge are shown in figures.

Electric Flux

Consider an arbitrary closed surface A in an electric filed E. Let the surface be divvied into a large number of elements, each of area dA. Each elementary area dA is so small that it is practically flat and the electric field intensity E within the surface is practically constant. Let the direction of E make angle θ with PN, the normal to dA. The normal PN is drawn so as to be directed away from dA. It is called the outward drawn normal to dA at P. The component of the elementary area dA, perpendicular to E is dAcosθ . Since the intensity of the electric field is E, the number of lines of force passing normally through unit are E. Therefore the number of lines of force passing normally through the area dAcosθ is EdAcosθ. This quantity is called the normal electric elementary areas and the sum taken, it gives the total outward normal flux of E over the area A.

It is given by Φ = ΣEdA Cosθ = EA Cos θ

Using Vector notation, it may be expressed as Φ = E.A

Gauss’s Theorem

It has been shown that electric flux is associated with electric field. But electric field arises from electric charge. So there is close relationship between electric charge and electric flux. Gauss’s theorem gives a relation between the flux through any closed surface and the net charge enclosed within the surface. The theorem may be stated as follows: The total flux of the electric field (also called total normal induction) over a closed surface is 1/e0 times the net charge enclosed by the surface. That is, the total electric flux over a closed surface enclosing charge q in free space is given by,
Φ = q/Є0
The closed surface taken in the electric field is called Gaussian surface.

Electric dipole and dipole moment

Two equal and opposite point charges separated by a small distance is called an electric dipole.

The product of one of the charges and the distance between the charges is called the electric dipole moment.

Let two charges +q and –q be separated by a small distances 2a. Then the electric dipole moment, p = q.2a
= 2a.q

The electric dipole moment is a vector directed along the axis of the dipole from the negative4 to the positive charge.

Electric Potential.

Consider a region free of any electric charge. Let a small charge +q be placed at any point in this region. It can be made to move about anywhere in the region without doing any work because this charge does not experience any electrical force.
To consider another case. Let a charge +q be placed in a region. Thus an electric field is produced around +q. Let a charge +q be introduced into this region. Now to move the charge +q from one point to another, work has to be done since this charge +q experiences a force of repulsion due to the presence of +q. Thus the presence of charge +q in the medium confers a property to each point of the medium by virtue of which work becomes necessary to move an electric charge up to that point. This property is called electrostatic or electric potential.

Usually the earth and the bodies connected to the earth by a conductor (earthed) are considered to be at zero potential. The potentials of other bodies are measured relative to the potential of the earth.

Electric potential at appoint is measured by the work done in taking unit positive charge from infinity (or zero potential) to that point.

The unit of electric potential is the volt.


The volt

The potential at a point is one volt if the work done in taking one coulomb of charge from infinity up to that point is one joule.

Ie, volt = joule/coulomb

Dimensions of potential

Potential = Work/Charge

Dimensions of Potential = Dim of work/Dim. of charge
= M1L2T-2/IT (Charge = Current x Time )

Therefore Dimensions of potential are M1L2I-1T-3

Potential Difference ( Pd )

The potential difference between two points in an electric field is measured by the work done in taking unit positive chare between those points.

Pd is also measured in volt.

Relation between intensity of electric field and potential – Intensity is Negative potential gradient.

Let E be the electric intensity at a point B due the presence of an electric charge +q at any point A. This field E acts along AB.

The force acting on the unit positive charge place at the point B is E. Then the work done in moving the unit positive charge from B to C, towards A, through a small distance dx can be given by
W = - E dx
The – sings shows that the work done is against the direction of the field. But this work done gives the potential difference dV between B and C
DV = -Edx
Ie E = -dv/dx
Dv/dx is the change of potential with respect to the distance. It is called the potential gradient. Thus from equn it amy he said that the intensity of electric field at any point is the negative potntail gradient at aht point. Or electric field may be represented as numerically equal to the p space rate of change of lelectrric potential.

The Electron Volt

Let V be the potential difference between two point sin an electric field, ie, the work done in moving unit positive charge between these points is V. Threfore the work required in moving a charge q between these points in the electric fild is qV. This work done will be stored in the charge as its energy. Hence the energy acquired by a charge q in moving between twopoints in an electric field under a potential difference V volts is qV Joules.

Thus, the energy acquired by an electron of charge e coulomb in moving between two points under a potential difference V volts = ev Joules. If V = 1 volt, the energy acquired by the electrons becomes e joules. This quantity I staken as a unit to measure the energy of charged particles and is called the electron volt. ( ev)

An electron volt is the energy acquired by an electron when it moves under a potential diference of oen volt.

1 ev = e Joules = 1.6021 x 10-19 J.

Electric Field due to a point charge

Let a point charge q be placed at a point in free space. This charge produces an electric field.

Let B be a point at a distance r from A. The intensity E of the electric field at B is to be determined.

Let a charge Q be placed at B. By Coulomb’s law, the force on this charge is given by

From this equation it is clear that the electric field at a point due toa point charge is iversily proportional to r2.

If the charge is in a medium of relative permittivity er, the intensity of the field is given by

The field acts along the line joining the point charge q and the point B. If the charge q is positie, the direction of the field will e away from the charge and if it is negative the field will e towards the charge.
 

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