18.5 Electric Potential

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Define electric potential at a point as the work done per unit positive charge in bringing a small test charge from infinity to that point.
  2. Recall and use the fact that the electric field at a point equals the negative of the potential gradient at that point.
  3. Use the formula V = Q / (4πε₀r) to calculate electric potential due to a point charge.
  4. Understand how electric potential leads to electric potential energy of two point charges, and use Eₚ = Qq / (4πε₀r).

1. Defining Electric Potential

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What is Electric Potential?

Imagine you are far, far away from a charge — so far away that the charge has no effect on you whatsoever. Physicists call this point infinity. At infinity, the electric potential is defined as zero.

Now, if you slowly move a tiny positive test charge from infinity toward another charge, you either have to do work (push against a force) or the field does work for you (pulls the charge along). The amount of work done per unit of positive charge during this journey is called the electric potential at that point.

Definition: Electric potential (V) at a point is the work done per unit positive charge in bringing a small positive test charge from infinity to that point.

In equation form:

V=WqV = \frac{W}{q}

Where:

  • V = electric potential (unit: volts, V, or J C⁻¹)
  • W = work done (unit: joules, J)
  • q = the test charge (unit: coulombs, C)

Electric potential is a scalar quantity — it has size but no direction. This makes it easier to work with than electric field strength, which is a vector.

Sign of Electric Potential

The sign of V tells you something important about what is happening:

  • Near a positive charge: The electric field pushes a positive test charge away. To bring a test charge toward a positive charge from infinity, you must push against this repulsion — so you do work on the charge. This means work done is positive, so V is positive.

  • Near a negative charge: The electric field attracts a positive test charge. Moving a test charge from infinity toward a negative charge means the field does the work for you. Work is done by the field, so V is negative.

Think of it like hills and valleys:

  • A positive charge creates a "hill" — you need energy to climb toward it.
  • A negative charge creates a "valley" — you fall toward it and release energy.

Important: The reference point is always infinity, where V = 0.

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