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1. Electric Potential Energy:
Definition, Electric Potential of a
Point and Multiple Charges

2. Electric potential energy is possessed by an object by
virtue of two elements, those being the charge possessed by
an object itself and the relative position of an object with
respect to other electrically charged objects. The magnitude
of electric potential depends on the amount of work done
in moving the object from one point to another against the
electric field.
When an object is moved against the electric field, it gains
some amount of energy which is defined as the electric
potential energy. For any charge, the electric potential is
obtained by dividing the potential energy by the quantity of
charge.

3. What Is Electric Potential Energy?
The electric potential energy of any given charge or system of changes is
defined as the total work done by an external agent in bringing the charge or
the system of charges from infinity to the present configuration without
undergoing any acceleration.
Definition: Electric potential energy is defined as the total potential energy a
unit charge will possess if located at any point in outer space.
Electric potential energy is a scalar quantity and possesses only magnitude
and no direction. It is measured in terms of Joules and is denoted by V. It
has the dimensional formula of ML2T-3A-1.

5. Electric Potential Formula
A charge placed in an electric field possesses potential energy and is measured
by the work done in moving the charge from infinity to that point against the
electric field. If two charges, q1 and q2, are separated by a distance d, the electric
potential energy of the system is:
U = [1/(4πεo)] × [q1q2/d]
If two like charges (two protons or two electrons) are brought towards each other,
the potential energy of the system increases. If two unlike charges, i.e., a proton
and an electron, are brought towards each other, the electric potential energy of
the system decreases.

8. Electric Potential Formula
The electric potential at any point around a point charge q
is given by:
V = k × [q/r]
Where,
•V = electric potential energy
•q = point charge
•r = distance between any point around the charge to the
point charge
•k = Coulomb constant, k = 9.0 × 109 N

10. The electrostatic potential between any two arbitrary charges q1,
q2 separated by distance r is given by Coulomb’s law and
mathematically written as:
U = k × [q1q2/r2]
Where,
•U is the electrostatic potential energy
•q1 and q2 are the two charges
Note: The electric potential at infinity is zero (as r = ∞ in the above
formula).

11. Electric Potential of a Point Charge
Let us consider a point charge ‘q’ in the presence of another charge ‘Q’ with
infinite separation between them.
UE (r) = ke × [qQ/r]
where, ke = 1/4πεo = Columb’s constant
Let us consider a point charge ‘q’ in the presence of several point charges
Qi with infinite separation between them.
UE (r) = ke q × ∑n
i = 1 [Qi /ri]

12. •At a point midway between two equal and opposite charges, the
electric potential is zero, but the electric field is not zero.
•The electric potential at a point is said to be one volt if one
joule of work is done in moving one Coloumb of the charge
against the electric field.
•If a negative charge is moved from point A to B, the electric
potential of the system increases.
•The reference level used to define electric potential at a point is
infinity. It signifies that the force on a test charge is zero at the
reference level.
•The surface of the earth is taken to be at zero potential since
the earth is so huge that the addition or removal of charge from it
will not alter its electrical state.

13. What Is Electric Potential Difference?
In an electrical circuit, the potential between two points (E) is
defined as the amount of work done (W) by an external agent in
moving a unit charge (Q) from one point to another.
Mathematically we can say that,
E = W/Q
Where,
•E = Electrical potential difference between two points
•W = Work done in moving a charge from one point to another
•Q = Quantity of charge in coulombs

14. FINAL PERFORMANCE TASK

15. Imagine you are an engineer working for a
technology company that specializes in
developing innovative solutions using electric
potential concepts. Your task is to design a
hypothetical application or device that utilizes
electric potential in a creative and practical way.
Your design should include the following
components:

16. Application/Device Description (10 points):
Provide a detailed description of the application
or device.
Explain its purpose and how it utilizes electric
potential.
Describe the problem it solves or the benefit it
provides.

17. Design Concept (15 points):
Create a diagram or sketch of your
application/device.
Label key components that relate to electric
potential (e.g., charges, potential difference, electric
field lines).
Explain the design choices you made and how
they contribute to the functionality of the
application/device.

18. Design Concept (15 points):
Create a diagram or sketch of your
application/device.
Label key components that relate to electric
potential (e.g., charges, potential difference, electric
field lines).
Explain the design choices you made and how
they contribute to the functionality of the
application/device.

19. Calculations and Analysis (15 points):
Include calculations related to electric potential
and potential energy in your design.
Show how these calculations are relevant to the
performance or operation of your application/device.
Discuss any assumptions you made in your
calculations.

20. Real-World Applications (5 points):
Research and provide at least one real-world
example where similar principles of electric potential
are used.
Explain how your design is inspired by or differs
from existing applications.

21. Submission Requirements:
The submission should be in the form of a PowerPoint
presentation or a written report.
Include clear diagrams, calculations, and explanations.
Submit the completed presentation/report via email
by the deadline.
The deadline for submission is until May 5, 2024