## Electric Charges And Fields

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1

## 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.
A ball of charge is placed in a hollow conducting uncharged sphere. After this, the sphere is connected with earth for a short time and the ball has not been brought into contact with the sphere. What charge will the sphere have after these operation? Where and how will this charge be distributed?
When a body is charged by induction, then the body
A
becomes neutral
B
does not lose any charge
C
loses whole of the charge on it
D
loses part of the charge on it
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## Vector form of coulomb's law

According to Coulomb's Law, electrostatic force on due to  is given by:

where
Permittivitty of the medium
and : Magnitudes of Charges
Distance between charges
Unit vector directed from to
How did Coulomb find the law of value of electric force between two point charges ?

Two charges each of micro coulomb are separated in a medium of relative permittivity  by a distance of . The force between them is :

A
B
C
D
3

## Properties of electric field lines

The field lines follow some important general properties:
(i) Field lines start from positive charges and end at negative charges. If there is a single charge, they may start or end at infinity.
(ii) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks.
(iii) Two field lines can never cross each other. (If they did,the field at the point of intersection will not have a unique direction, which is absurd.)
(iv) Electrostatic field lines do not form any closed loops.

Drawings I and II show two samples of electric field lines. Then :

A
the electric fields in both I and II are produced by negative charge located somewhere on the left and positive charges located somewhere on the right
B
in both I and II the electric field is the same everywhere
C
in both cases the field becomes stronger on moving from left to right
D
the electric field in I is the same everywhere, but in II the electric field becomes stronger on moving from left to right
Two electric field lines cannot cross each other. Also, they cannot form closed loops. Give reasons.
4

## Electric flux

Electric flux is the measure of flow of the electric field through a given area. Electric flux is proportional to the number of electric field lines going through a normally perpendicular surface.
Define electric flux. Write its SI unit.
The area of a metallic plate is . A charge of is given to the plate. Determine the electric filed intensity at a point near to the plate.
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## Electric field due to a dipole

where is the  angle between the distance vector and dipole.
Derive an expression for electric field due to an electric dipole at a point on its axial line.
Two point dipoles and are located at (0,0,0) and (1m,0,2m). Find the field at the point (1,0,0).
A
B
C
D
none of these
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## Electric field due to an infinite linear charge distribution

We have the charge enclosed by the
cylinder. Because the linear charge density (charge per unit length, remember) is
uniform, the enclosed charge is h.Thus, Gauss law

where is the linear charge density and r is the distance at which the electric field is to be calculated.
Use Gauss's theorem to find the electric field due to a uniformly charged infinitely large plane thin sheet with surface charge density .
The region between two concentric spheres of radii 'a' and 'b', respectively(see figure), has volume charge density , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :
A
B
C
D