Electric Potential

Confusing concepts?

Concepts and terms on this page are explored more intuitively in the Altitude Analogy page. If you're confused like I was, give it a read if you haven't already!

Electric Field Strength

Electric field strength is a vector which represents the electrical force per unit of positive charge - similar to how gravitational field strength is the weight per unit of mass. It is analogous to gravitational field strength for gravitational fields.

The electric field strength can be calculated at the point of a test charge, if the charge and mass of the particle is known:

Formula

$E = \frac{F}{Q}$

Variable Key

$E$ is the electric field strength, in newtons per coulomb.
$F$ is the electrostatic force acting on the particle, in newtons.
$Q$ is the charge of the particle being acted on, in coulombs.

Radial Fields

Substituting $F$ with Coulomb's law causes the charge of the particle, $Q$ , to cancel out with one of the charges in the numerator - which leaves us with the below formula for radial fields:

Formula

$E = \frac{Q}{4 π ε_{0} r^{2}}$

Variable Key

$E$ is the electric field strength, in newtons per coulomb.
$Q$ is the ⚠️ charge of the particle creating the field, in coulombs.
$ε_{0}$ is the vacuum permittivity constant.
$r$ is the distance to the particle, in metres.

Charge Confusion!

This below formula can only be used for radial fields - it's essentially just the Coulomb's law formula but with one of the particles removed, hence leaving behind a radial field.

In this formula, $Q$ refers to the charge of the particle which is creating the field you're measuring - any test charge that may be situated at the point you're trying to measure the electric field strength of doesn't matter!

Electric Potential

The electric potential at a point (sometimes referred to potential within an appropriate context) is a scalar which represents electric potential energy (the electric counterpart to gravitational potential energy) per unit of charge. This can be positive or negative depending on the polarity of the charge creating the electric field.

The formal definition of electric potential at a point is the energy required to move a 1 coulomb positive test charge to that point from an infinitely far location, where the electric field strength would be zero. This helps to explain why the electric potential at a point increases when it approaches a positively charged particle, and not vice versa.

Electric potential is the electric counterpart to gravitational potential, and both use the symbol $V$ .

Formula

$V = \frac{W}{Q}$

Variable Key

$V$ is the electric potential at a point, in joules per coulomb.
$W$ is the work done bringing a positive test charge from infinity, in joules.
$Q$ is the charge of the particle brought to the point, in coulombs.

Wait, isn't this just voltage?

Does this look familiar from the Higher Physics course? While this is the same formula for voltage or potential difference, the term "voltage" can be confusing, since as the name "potential difference" suggests it describes only differences in electric potentials. This is why you'll never see it on an SQA Advanced Higher exam paper! Despite you having most likely used the term up until this point in physics, now would be a good time to stop and forget using the term altogether, and reframe what you knew about voltage in the context of differences in electric potential. Ah, the joy of SQA Physics :D

Electronvolts

If we rearrange the formula for electric potential, we get $W = V Q$ , which shows that energy can be expressed as potential multiplied by charge. This is what the electronvolt is - a unit of energy which represents the work done to move an electron through a potential difference of 1 joule per coulomb. The symbol for electronvolts is $eV$ .

You should have already been introduced to electronvolts at Higher level, however hopefully this reintroduces them in a context which makes more intuitive sense and gives you a better understanding of the unit.