Short Answer:

Electric potential is the amount of work needed to bring a unit positive charge from infinity to a point in an electric field. It is a measure of the energy stored per unit charge at that point. Electric potential is a scalar quantity and is measured in volts (V).

The electric field, on the other hand, shows the force experienced by a unit positive charge placed at a point. It is a vector quantity and has both magnitude and direction. While electric potential tells us how much energy a charge has at a point, the electric field tells us how strongly the charge will be pushed or pulled.

Detailed Explanation:

Electric potential and electric field difference

Electric potential and electric field are two closely related but different concepts in electrostatics. Both deal with the effect of electric charges on the space around them, but they explain different physical ideas.

Electric potential

Electric potential at a point in space is defined as the work done in bringing a unit positive test charge from a reference point (usually infinity) to that point without acceleration. It tells us how much electric potential energy is available per unit charge at a point in the field.

Formula:

V=WqV = \frac{W}{q}V=qW​

Where:

• V = electric potential (in volts)
• W = work done (in joules)
• q = test charge (in coulombs)

For a point charge, electric potential at distance r is:

V=14πε0⋅QrV = \frac{1}{4\pi\varepsilon_0} \cdot \frac{Q}{r}V=4πε0​1​⋅rQ​

This formula shows that the potential decreases as we move farther from the charge.

Electric field

The electric field is a measure of the force per unit charge at a point. It shows how strongly a test charge would be pushed or pulled at that point due to the presence of another charge.

Formula:

E=FqE = \frac{F}{q}E=qF​

Or, when using potential:

E=−dVdrE = -\frac{dV}{dr}E=−drdV​

This means the electric field is the rate of change of electric potential with distance. The negative sign indicates that the electric field points in the direction of decreasing potential.

Key differences

1. Nature:
   • Electric potential is a scalar quantity (has magnitude only).
   • Electric field is a vector quantity (has both magnitude and direction).
2. Meaning:
   • Electric potential tells how much energy per charge is stored at a point.
   • Electric field tells the strength of force acting on a unit charge.
3. Units:
   • Electric potential is measured in volts (V).
   • Electric field is measured in newtons per coulomb (N/C) or volts per meter (V/m).
4. Relation:
   • Electric field is the spatial rate of change of electric potential.

Real-life example

Think of electric potential like the height of a hill, and the electric field like the slope.

• A higher point (potential) means more energy.
• A steeper slope (field) means more force acting on a rolling object (charge).

This comparison helps to understand why a charge moves from high potential to low potential—just like a ball rolling downhill due to gravity.

Conclusion:

Electric potential measures how much potential energy a unit charge has at a point, while electric field measures the force that the charge would feel. One is scalar, and the other is vector. Both are related, but they describe different aspects of how charges influence space and each other. Understanding both concepts is essential in analyzing electric circuits and fields.