Question

distinguish between electric potential and potential energy and write the relation between them​

Answer 1

The basic difference between electric potential and electric potential energy is that Electric potential at a point in an electric field is the amount of work done to bring the unit positive charge from infinity to that point, while electric potential energy is the energy that is needed to move a charge against the electric field.

The gravitational potential at a point in the gravitational field is the gravitational potential energy of a unit mass placed at that point. In this way, the electric potential at any point in the electric field is the electric potential energy of a unit positive charge at that point.

If W is the work done in moving a unit positive charge q from infinity to a certain point in the field, the electric potential V at this point is given by:

V = W/q

It implies that electric potential is measured relative to some reference point and like potential energy we can measure only the change in potential between two points.

Electric potential is the scalar quantity. Its unit is volt which is equal to joule per coulomb (J/C).

Definition of volt

If one joule of work done against electric filed to bring the unit positive charge from infinity to the point in the electric field then potential difference at that point will be one volt.

Electric potential energy

To apply the law of conservation of energy, we need to define electric potential energy, potential energy can be defined only for conservative force. The work done by a conservative force in moving an object between any two positions is independent of the path taken. The electrostatic force between any two charges is conservative because the dependence of on positions is just like the gravitational force which is a conservative force. Hence we can define potential energy for electrostatic force.

We know that the change in potential energy between any two points, a and b equals the negative of work done by the conservative force on an object as it moves from point a to point b:

Δ P.E = -W

Hence we define the change in potential energy (P.Eb – P.E a), when a point charge q moves from some point a to another point b.As the negative of the work done by the electric force on charge as it moves from point a to b.

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Answer 2

Electric potential (V) is the work done to bring a unit test charge from infinity to a fixed point. Electric potential energy (U) is the energy required to carry out this process.

• Electric potential is the work done.
• Electric potential energy is the energy required to do the work.
• Formula of electric potential is V = $\frac{kq}{r}$
• Formula of electric potential energy is U = $\frac{kq1q2}{r12}$
• Where q, q1, and q2 are charged.
• r is the distance between charges.
• r12 is the distance between two charges.
• Both are vector quantities.
• Electric potential is the sum of potential at different positions due to charge q
• Electric potential is the sum of potential energies due to different pairs of charges.