Absolute Potential
In electrostatics, absolute potential (also called electric potential at a point) is the amount of work done per unit positive charge in bringing a test charge from infinity to that point without acceleration.
Definition
V = W / q
Where:
- V = absolute potential (volts)
- W = work done in bringing the charge (joules)
- q = test charge (coulombs)
For a point charge Q, the absolute potential at distance r is:
V = (1 / 4πε₀) × (Q / r)
Here:
- Q = source charge
- r = distance from the charge
- ε₀ = permittivity of free space
- 1 / 4πε₀ = 9 × 10⁹
So we usually write:
V = (9 × 10⁹ × Q) / r
Important Points
- Potential is a scalar quantity.
- Unit: Volt (V).
- At infinity, potential is taken as zero.
- Positive charge gives positive potential; negative charge gives negative potential.
Example
Find the absolute potential at 2 m from a charge of 4 μC.
Given:
- Q = 4 × 10⁻⁶ C
- r = 2 m
V = (9 × 10⁹ × 4 × 10⁻⁶) / 2
V = 18 × 10³ V
V = 18000 V
Therefore, the absolute potential is 18 kV.