# Electric Potential

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:

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

### Radial Fields

Substituting **radial fields**:

is the **electric field strength**, in newtons per coulomb.is the ⚠️ **charge of the particle creating the field**, in coulombs.is the **vacuum permittivity**constant.is the **distance to the particle**, in metres.

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, **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

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

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 **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

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.