Hello friends in this article we will know that Electricity What is electric potential? And what is the electric potential due to a point charge? And what is the electric potential due to multiple charges? What is the potential due to an electric dipole? And what is an equipotential surface and will know many facts related to it.
Consider the very small displacement dl (from point A to B) of a test charge q at an angle α with the electric field. The force qE exerted by the electric field on the test charge is. Its component in the AB direction is qEcosα. If a charge is applied from A to B, then the work done on the field dW is equal to the product of force and displacement.
dW = qEcosα.dl = qE.dl
Here dl is the vector in the direction from A to B.
The work W required by the electric field to move the test charge q from A to B can be found by dividing the distance AB into several smaller parts. This work can be represented by the following line intergral.
W = q E.dl
In a test charge, there is some potential energy due to its presence in the electric field. This work is equal to W. The potential energy of a unit charge can be found by dividing W by q. The potential difference between points A and B is V.
If VAB is positive then the charge has kinetic energy from A to B i.e. the field does work.
If VAB is negative, then in the movement of charge from A to B, potential energy is gained i.e. work is done by an external agency.
Electric potential due to point charge
r distance electric potential from a point charge q –
The intensity of the electric field is equal to the change in potential with distance, so the intensity can also be called the potential gradient.
Hence, the potential gradient,
E = q/4πε0εr V/m
If the potential is known for all points in the space, then the constituent types of E can be found-
Electric potential due to a group of charges
The potential at a point due to a set of charges (q1, q2, q3, ……….qn ) is equal to the sum of the individual potentials due to each charge.
If the description of charge is continuous, then the potential at any point is
Here dq is a superfine charge at a distance r from the point.
Dipole in an electric field
An electric dipole consists of two equal but opposite charges (q) at a very short distance (a), the moment p (moment) of the dipole is one, its value is 2aq. The direction of the moment is from negative to positive charge.
When a dipole is placed in a uniform electric field E, equal but opposite forces act on both the charges of the dipole. Thus, the net force on the dipole is zero but on the dipole a torque acts about the axis. These attractions are in the vertical direction of this page.
T = F (2a sinθ)
, (qE)(2a sinθ)
= 2aq E sinθ
= pE sinθ
In vector form,
= p × E
Here p is the dot product of E.
Some work has to be done to change the position of the dipole in the electric field. This work is stored in the system as potential energy.
The potential energy required to rotate the dipole at θ° from its normal position,
Potential due to an Electric Dipole
Potential due to dipole at point P from Fig.
Electrical Potential Energy
If two charges q1 and q2 are placed at a distance r from each other, then energy is stored in this system. A certain work needs to be done to move these charges away from each other. If the charges are of opposite nature then their position energy gets converted into kinetic energy and they get accelerated towards each other.
Thus the potential energy of a system of point charges is equal to the work done in bringing them closer to each other from infinity.
Potential energy due to charge q1,
V = (1/4πε0)(q/r)
The work done in bringing the charge q2 from infinity to q1 at a distance r,
W = Vq2
Hence, the potential energy of the system,
U = q2V
It is a surface whose potential is the same at all points, the potential gradient on such a surface is zero and no component of the electric field is along the surface. Lines of force always line the Equipotential surface at 90°.
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