# Electrostatics

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## Electrostatics

Charge

Charge is that property of an object by virtue of which it apply electrostatic force of interaction on other objects.

Charges are of two types

(i) Positive charge

(ii) Negative charge

Like charges repel and unlike charges attract each other.

Quantization of Charge

Charge on any object can be an integer multiple of a smallest charge (e).

Q = ± ne

where, n = 1, 2, 3,……. and e = 1.6 * 10-19 C.

Conservation of Charge

Charge can neither be created nor be destroyed. but can be transferral from one object to another object.

Recently a new particle has been discovered called ‘Quark’. It contains charge ± e / 3, ± 2e / 3.

[The protons and neutrons are combination of other entities called quarks, which have charges 1 / 3 e. However, isolated quarks have not been observed, so, quantum of charge is still e. ]

Coulomb’s Law of Electrostatics

Electrostatic force of interaction acting between two stationary charges is given by

F = 1 / 4π εo q1q2 / r2

where q1, q2 are magnitude of point charges, r is the distance between them and εo is permittivity of free space.

Here, 1 / 4πεo = (10-7 N – s2 / C2)C2

Substituting value of c = 2.99792458 X 108 m/s,

We get 1 / 4πεo = 8.99 x 109N-m2/C2

In examples and problems we will often use the approximate value,

1 / 4πεo = 9 * 109N-m2/C2

The value of εo is 8.85 * 10-12 C2 / N-mC2.

If there is another medium between the point charges except air or vacuum, then εo is replaced by εoK or εoεr or ε.

where K or εr is called dielectric constant or relative permittivity of the medium.

K = εr = ε / εo

where, ε = permittivity of the medium.

For air or vacuum, K = 1

For water, K = 81

For metals, K = ∞

Coulomb’s Law in Vector Form

Force on q2 due to q1,

The above equations give the Coulomb’s law in vector form.

Force on q1 due to q2 = – Force on q2 due to q1

F12 = – F21

F12 = q1q2 / 4πε . r1 – r2 / |r1 – r2|3

The forces due to two point charges are parallel to the line joining point charges; such forces are called central forces and electrostatic forces are conservative forces.

Electric Field

The space in the surrounding of any charge in which its influence can be experienced by other charges is called electric field.

Electric Field Lines

“An electric field line is an imaginary line or curve drawn through a region of space so that its tangent at any point is in the direction of the electric field vector at that point. The relative closeness of the lines at some place give an idea about the intensity of electric field at that point.”

Two lines can never intersect.

Electric field lines always begin on a positive charge and end on a negative charge and do not start or stop in mid space.

Electric Field Intensity (E)

The electrostatic force acting per unit positive charge on a point in electric field is called electric field intensity at that point.

Electric field intensity E =

Its SI unit is NC-1 or Vim and its dimension is [MLT-3 A-1].

It is a vector quantity and its direction is in the direction of electrostatic force acting on positive charge.

Electric field intensity due to a point charge q at a distance r is given by

E = 1 / 4π εo q / r2

Electric Potential (V)

Electric potential at any point is equal to the work done per positive charge in carrying it from infinity to that point in electric field.

Electric potential, V = W / q

Its SI unit is J / C or volt and its dimension is [ML2T-3A-1].

It is a scalar quantity.

Electric potential due to a point charge at a distance r is given by

v = 1 / 4π εo q / r

The rate of change of potential with distance in electric field is called potential gradient.

Potential gradient = dV / dr

Its unit is V / m.

Relation between potential gradient and electric field intensity is given by

E = – (dV / dr)

Equipotential Surface

Equipotential surface is an imaginary surface joining the points of same potential in an electric field. So, we can say that the potential difference between any two points on an equipotential surface is zero. The electric lines of force at each point of an equipotential surface are normal to the surface.

(i) Equipotential surface may be planer, solid etc. But equipotential surface can never be point size.

(ii) Electric field is always perpendicular to equipotential surface.

(iii) Equipotential surface due to an isolated point charge is spherical.

(iv) Equipotential surface are planer in an uniform electric field.

(v) Equipotential surface due to a line charge is cylindrical.

Electric Lines of Force

Electric lines of force are the imaginary lines drawn in electric field at Which a positive test charge will move if it is free to do so.

Electric lines of force start from positive charge and terminate on negative charge.

A tangent drawn at any point on electric field represents the direction of electric field at that point.

Two electric lines of force never intersect each other.

Electric lines of force are always perpendicular to an equipotential surface.

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