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The magnitude of the force of attraction or repulsion
between two point charges q1 and q2 separated by a
distance 'r' is given by
4p Î0 r2
k = dielectric
Î0 = permittivity
of free space
Î = k Î 0 = permittivity
of the medium
Field Intensity (E)
The electric field intensity at a point in an electric field
is defined as the force exerted on a unit positive charge placed at that
Also, E =
1. Electric field due to one or more charges can be picturised
by drawing the lines of force.
2. A line of electric force is defined as the imaginary line or path
along which a free positive charge travels when placed in an electric
3. These lines start from a positive charge and terminate at a negative
4. They never cross each other and at any one point, an electric field
can have only one direction.
5. They normally leave the surface of a charged body.
6. The magnitude of an electric field intensity
at a given point is given by the number of electric lines of force
passing normal to the unit area drawn around the point.
Electric flux through any surface
in an electric field is defined as the normal component of the lines of
force passing through that surface.
The lines of force in a region indicate the magnitude and the direction
of electric field.
Electric field intensity E =
\ Æ = EA
perpendicular to surface area.
If the electric field intensity is
at an angle q with the normal to a surface area ds,
then the electric flux through the surface in normal
direction is f
= E A Cos q
= E Cos q dS
Normal Induction (T.N.E.I.)
The total number of lines of
induction leaving a closed surface normally is called total normal
(dielectric constant × Î0) × (component
of field intensity normal to the surface) × (area of the surface)
a small surface element of a positively charged conductor. The lines of
force originating from various points on this surface element form a
group called a tube of force. The lines of force lie on the surface of
the tube of force. The ends of the tube of force are those areas from
where the lines of force originate and terminate as shown in the fig.
If the surface elements are so chosen that the charge on each element
is one unit, then the tube of force is called Unit tube of force or
number of tubes of force originating from a charge depends on the
permittivity of the medium. In order to show that number of tubes of force
does not depend on the nature of the medium, Faraday induced the concept
of induction. According to him, only one tube originates to form a unit
positive charge, whatever be the medium
surrounding this charge. Such a tube is called a tube of induction.
Angle and Solid Angle
The angle q in a plane is given by the ratio of the arc which
subtends the angle q to the radius r.
It is measured in radian.
If the area ds subtends a solid angle dw at 'O' and q is the angle
between the line joining O with the centre of the area and normal to the
Total normal electric induction
(T.N.E.I.) through any imaginary closed surface is equal to the total
quantity of charge enclosed in that surface.
The total electric flux through a closed surface is equal to
1/e times the
algebraic sum of the charges enclosed by that surface.
Suppose a charge (+Q) is situated at some point O within a closed surface
S. Consider a small element of area ds on the surface S.
Take a point P on the small element which is at a distance r from the
point O. The electric field intensity at point P due to charge +Q is
unit normal to the area dS, then the electric flux over the area dS is
Using (1), we get,
\ Electric induction over the area dS
But ds. cosq/r2
= Solid angle dw subtended by
the area dS at O.
.. Electric induction over the area dS =
Total normal electric induction over a
closed surface S
But Sdw = 4p = Total solid angle subtended
by the closed surface at O
Total normal electric induction over a closed
If Q1, Q2, Q3…. are the
within the closed surface then
= Q1 + Q2 + Q3 + ……..
= S Qi
of Gauss Law
(i) The electric
intensity due to a uniformly charged sphere at any point outside the
Î = k Î0, k :
dielectric constant of the medium.
q : total charge
r : distance of
the point from the centre of the sphere.
R : radius of the sphere.
Case I : Sphere having uniform surface
charge density s, and for a point very close to the charged sphere, E =
Case II : For a point inside the charged sphere, E = 0.
(ii) Electric intensity at any point outside a uniformly charged cylinder
q : charge per
perpendicular distance of the given point from the axis of the cylinder
R : radius of the cylinder.
If the point is very close to the charged cylinder.