Electric Potential: A Quantitative Approach

• Unit of work (W) = joule (J)
• Unit of charge (q₀) = coulomb (C)
• So, unit of potential = joule/coulomb = volt (V)

1 V = 1 J/C

Meaning: If 1 joule of work is done in bringing a 1 coulomb test charge from infinity to a point, the potential at that point is 1 volt.

Dimensional Formula

Electric potential describes the "electrical state" of a conductor — it decides the direction in which charge will flow if the conductor is connected to another one.

Flow analogies:

Just as liquid flow and heat flow don't depend on the amount of liquid or heat but only on level/temperature, the flow of positive charge doesn't depend on the amount of charge — only on the potential difference.

(a) Why Infinity Is Preferred (Theoretical Electrostatics)

• Uniformity: Infinity is a region where the influence of charges vanishes, giving a universal, consistent reference free from local charge distributions.
• Mathematical simplicity: For a point charge, V = \[\frac {kq}{r}\]​. As r → ∞, V → 0, making it a natural reference.
• Ideal for isolated charges: Works well for single charges or free-space systems where the field is negligible far away.

(b) Why Earth's Potential Is Taken as Zero (Practical Applications)

• Practical reference: Earth is an enormous conductor that can absorb or supply large amounts of charge with negligible change in its own potential.
• Grounding in circuits: Earth provides a stable, easily accessible potential for grounding, simplifying circuit design and measurement.

(c) Why Earth Isn't Used as the Universal Reference Instead of Infinity

• Earth is not an absolute zero-potential reference in space — it carries a net charge and interacts with cosmic electric fields.
• Context matters:
  In electrostatics → infinity is preferred (universal, unambiguous zero).
  In circuit theory/practical applications → Earth is preferred (accessible, stable, widely used for grounding).

• Electric potential (V) = work done per unit positive test charge, brought from infinity to a point without acceleration: V = \[\frac {W}{q_0}\].
• SI unit: volt (V) = 1 J/C.
• Dimensional formula: [ML²T⁻³A⁻¹]
• Positive charge flows from higher to lower potential — analogous to liquid flowing downhill or heat flowing from hot to cold.
• Infinity is the standard reference in theoretical electrostatics; Earth is the standard reference in practical circuits and grounding — each valid in its own context.