Difference Between Electric Field and Electric Potential
1. Basic Meaning
- Electric Field (E): Force per unit charge at a point (vector).
- Electric Potential (V): Potential energy per unit charge (scalar).
2. Mathematical Definitions
Electric Field
E = F / q
Units: N/C or V/m
Electric Potential
V = U / q
Units: Volt (V)
3. Mathematical Relationship
E = - dV/dx
This shows that electric field is the rate of change of potential.
4. Integral Form
V = - ∫ E · dr
Potential is obtained by integrating the electric field.
5. Example (Point Charge)
Electric Potential:
V = (1 / 4πε₀) × (Q / r)
Electric Field:
E = (1 / 4πε₀) × (Q / r²)
6. Summary Table
| Feature | Electric Field (E) | Electric Potential (V) |
|---|---|---|
| Nature | Vector | Scalar |
| Meaning | Force per charge | Energy per charge |
| Formula | E = F / q | V = U / q |
| Relation | E = -∇V | V = -∫E·dr |
| Units | N/C or V/m | Volt |
- Electric Field: How strongly a charge is pushed.
- Electric Potential: How much energy a charge has.