1. The Idea Behind Electric Potential
Electric potential is a way to describe how much electric energy a point in space has. If a positive test charge is placed at that point, electric potential tells us the amount of work needed to bring that charge from some reference point (usually infinity) to that point.
In simple words, electric potential shows how “energetically charged” a point is. A point with higher potential can push charges away more strongly.
1.1. Definition of Electric Potential
Electric potential at a point is defined as the work done to bring a unit positive charge from infinity to that point.
\( V = \dfrac{W}{q} \)
Here, V is potential, W is the work done, and q is the charge.
1.1.1. What This Really Means
If a point has high potential, it means a positive charge placed there has more electric energy. A lower potential means less electric energy.
2. Understanding Potential Difference (Voltage)
Charges begin to move only when there is a difference in potential between two points. This difference is called potential difference or voltage.
It plays the same role as pressure difference in pushing water through a pipe. Without pressure difference, water doesn't flow. Similarly, without potential difference, charges don't flow.
2.1. Definition of Potential Difference
Potential difference between two points is the work done in moving a unit positive charge from one point to the other.
\( V = W/q \)
Here the work is done between two points, not from infinity.
2.1.1. Why Charges Move
Charges move from a point of higher potential to a point of lower potential, just like water naturally flows from higher level to lower level.
3. A Simple Analogy to Visualise Potential
One of the easiest ways to understand electric potential is to compare it with height in a gravitational field.
- Higher height = more gravitational potential energy
- Higher electric potential = more electric potential energy for a charge
Just like a ball rolls downhill (from higher height to lower height), electric charges move from higher potential to lower potential.
3.1. Analogy for Potential Difference
If two water tanks are placed at different heights, water will flow from the tank at higher height. The flow stops when both tanks are at the same level.
Similarly, electric current flows only when there is a potential difference. When the potential difference becomes zero, current stops.
4. Relation Between Electric Potential and Electric Field
The electric field represents the force acting on a unit positive charge. Electric potential represents the energy per unit charge. These two quantities are related.
If we move a charge in the direction of the electric field, the potential decreases. If we move it opposite to the field, the potential increases.
4.1. Key Relation
The change in potential between two points is the negative of the work done by the electric field:
\( E = -\dfrac{dV}{dx} \)
This shows that electric field is the rate at which potential changes with distance.
5. Potential Difference and Current Flow
In an electric circuit, a battery maintains a constant potential difference between its terminals. This potential difference pushes charges and makes current flow.
The greater the voltage across a conductor, the greater the current that flows through it, provided the resistance remains the same.
5.1. Tiny Example
When a 9 V battery is connected across a wire, the potential at the positive terminal is 9 V higher than the potential at the negative terminal. This difference pushes electrons to move through the wire, creating electric current.