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
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.