Electric Potential and Potential Difference
In the Electricity chapter, electric potential and potential difference are two very important ideas. A clear understanding of them is needed to study batteries, electric current, circuits, electromotive force (EMF), resistance and Ohm's law.
Think of a cell or battery as a device that does not keep its two terminals at the same potential. The difference in potential between the two terminals is the potential difference. When the terminals are connected by a conductor, this potential difference produces an electric field and organised charge motion begins.
Remember: Electric potential is not the amount of charge on an object. It is a measure of work or electric potential energy per unit charge at a point.
1. What is Electric Potential?
Imagine placing a very small positive charge at a point in an electric field. Such a charge is called a test charge.
The electric potential at a point is the external work done in bringing a unit positive test charge slowly from infinity to that point.
where,
- = electric potential
- = work done
- = test charge
Thus, in a simple sense, the greater the potential at a point, the greater the work that may be needed to bring a unit positive charge there.
2. SI Unit of Electric Potential
The SI unit of electric potential is volt (V).
That is,
1 volt = 1 joule/coulomb
Meaning of 1 Volt
If 1 joule of work is required to move 1 coulomb of charge between two points, the potential difference between those two points is 1 volt.
3. Nature of Electric Potential
Electric potential is a scalar quantity. It has magnitude but no specific direction.
Its dimensional formula is
Since both work and charge are scalar quantities, their ratio, electric potential, is also scalar.
4. Higher and Lower Potential
Suppose the potentials at points A and B are and respectively.
If
then A is at higher potential and B is at lower potential.
An object cannot be called simply “at higher potential” or “at lower potential” only because it is positively or negatively charged. Potential depends on the reference point, distance and charge distribution.
5. Potential Difference
The difference in electric potential between two points is called potential difference.
If the potentials at A and B are and , then
If external work is done to move a positive test charge slowly from A to B, then
Therefore,
6. Electric Potential vs Potential Difference
| Electric Potential | Potential Difference |
|---|---|
| Refers to the potential at one particular point. | Refers to the difference in potential between two points. |
| Defined relative to a chosen reference point. | Compares two specified points. |
| Usually represented by V. | Usually represented by ΔV. |
| SI unit is volt. | SI unit is also volt. |
7. What Does Voltage Mean?
In electric circuits, the word voltage generally refers to the potential difference between two points.
For example, a 12 V battery generally means that the battery can maintain approximately 12 volts of potential difference between its terminals.
Voltage and electric current are not the same. Voltage is a difference in potential, while electric current is the amount of charge flowing per unit time.
8. Why Does Potential Difference Produce Electric Current?
A metallic conductor contains many free electrons. Without a potential difference, they move randomly and there is no net current in one particular direction.
When a battery or cell creates a potential difference across the conductor, an electric field is set up inside it. The free electrons then acquire a net drift in a definite direction.
Direction of Conventional Current
In a metallic conductor, conventional current is taken as:
higher potential → lower potential
Direction of Electron Drift
Electrons carry negative charge. Therefore, in a metallic conductor their drift is:
lower potential → higher potential
So electron drift is opposite to conventional current.
9. A Simple Water Analogy
The idea of water stored at different heights can help in understanding electric potential.
| Water | Electricity |
|---|---|
| Water at greater height may have more gravitational potential energy. | A unit positive charge at higher electric potential may have greater electric potential energy. |
| A difference in height can cause water to flow. | A potential difference helps produce organised motion of charge. |
| A pump can maintain a difference in height. | A battery or cell maintains potential difference. |
This is only an analogy for understanding the idea. Electric potential and height are not the same physical quantity.
10. Electric Potential Energy
If a charge is at a point of potential , its electric potential energy is
where,
- = electric potential energy
- = charge
- = electric potential
The change in potential energy between two points is
11. Electric Potential Due to a Point Charge
In vacuum, the electric potential at a distance from a point charge is
where,
Effect of the Sign of Charge
- If , the potential is positive.
- If , the potential is negative.
Here the potential at infinity is taken as zero.
Effect of Distance
Therefore, the magnitude of potential decreases as the distance from the point charge increases.
12. Relation Between Electric Field and Potential
The electric field generally points from higher potential to lower potential.
For a small displacement along the direction of a uniform electric field,
The negative sign shows that potential decreases in the direction of the electric field.
For Class 10, the key idea is: the electric field points from higher potential to lower potential.
13. Equipotential Surface
A surface on which electric potential is the same at every point is called an equipotential surface.
Between two points on an equipotential surface,
Therefore, the net electric work done in moving a charge along the surface is
Example
For an isolated point charge, concentric spherical surfaces around it may be considered equipotential surfaces.
14. How Does a Battery Maintain Potential Difference?
Inside a battery or cell, chemical reactions separate charges and create a potential difference between the terminals.
When the circuit is completed, this potential difference creates an electric field in the conductor and helps establish electric current.
How a battery supplies energy is discussed in more detail under Electromotive Force (EMF).
15. Solved Example 1: Finding Potential
Question: 20 J of work is required to bring 5 C of charge to a point. What is the electric potential at that point?
Given,
Therefore,
Answer: 4 V
16. Solved Example 2: Finding Work
Question: How much work is required to move 3 C of charge through a potential difference of 12 V?
Therefore,
Answer: 36 J
17. Solved Example 3: Electric Potential Energy
Question: A charge of is placed at a point of potential 50 V. Find its electric potential energy.
Therefore,
Answer:
18. Solved Example 4: Potential Due to a Point Charge
Question: What is the potential at a distance of 0.30 m from a point charge in vacuum?
Answer:
19. Everyday Examples of Potential Difference
Dry Cell
A common dry cell can provide a potential difference of about 1.5 V.
USB Power Supply
Many USB power supplies use a potential difference of 5 V.
9 V Battery
The nominal potential difference between the terminals of a familiar 9 V battery is about 9 V.
The actual terminal voltage of a battery may differ somewhat from its nominal value depending on state of charge, current and internal resistance.
20. Common Misconceptions
Mistake 1: Potential and Charge are the Same
No. Charge is measured in coulomb (C), while potential is measured in volt (V).
Mistake 2: Voltage Means Current
No. Voltage is potential difference, while current is the amount of charge flowing per unit time.
Mistake 3: Electrons Move from Higher Potential to Lower Potential
In a metallic conductor, electrons drift from lower potential to higher potential. Conventional current is in the opposite direction.
Mistake 4: Electric Potential is a Vector
No. Electric potential is a scalar quantity.
Mistake 5: A Battery Creates New Electrons
No. A battery does not create new electrons. It uses chemical energy to separate charge and maintain a potential difference.
Mistake 6: Electric Potential and Potential Difference are the Same
No. Electric potential is associated with one point, while potential difference is the difference between the potentials of two points.
21. Important Points for Exams
- Electric potential:
- SI unit: volt (V)
- Electric potential is a scalar quantity
- Potential difference:
- Electric potential energy:
- Potential due to a point charge:
- Conventional current: higher potential → lower potential
- Electron drift: lower potential → higher potential
22. Practice Questions
- If 24 J of work is done to move 4 C of charge, what is the potential difference?
- How much work is needed to move 5 C of charge through a potential difference of 6 V?
- The potentials at two points are 15 V and 9 V. What is their potential difference?
- What is the electric potential energy of a 3 μC charge at 200 V?
- Why are conventional current and electron drift in opposite directions?
- Explain the physical meaning of 1 volt in your own words.
- Why is electric potential a scalar quantity?
- How does potential change if the distance from a point charge is doubled?
- Why is the work done in moving a charge along an equipotential surface zero?
- How does a battery create the potential difference needed for electric current in a circuit?
23. Quick Revision
| Concept | Key Point |
|---|---|
| Electric Potential | Work or potential energy per unit charge |
| Formula | V = W/q |
| SI Unit | volt (V) |
| 1 volt | 1 J/C |
| Potential Difference | ΔV = VB − VA |
| Electric Potential Energy | U = qV |
| Point-Charge Potential | V = kQ/r |
| Nature | Scalar quantity |
| Conventional Current | Higher potential → lower potential |
| Electron Drift | Lower potential → higher potential |
In Short
Electric potential measures the work or electric potential energy per unit positive charge at a point.
The basic relation is
The difference between the potentials of two points is called potential difference or voltage. This potential difference helps create the electric field that maintains organised charge motion in a circuit.
Once this idea is clear, later topics such as Electromotive Force (EMF), Electric Current, Resistance and Ohm's Law become much easier to understand.
