 You might remember from your previous work that if you hold a pencil off the ground it has potential energy So where does this potential energy come from? Think about holding a pencil out in space Will it still have the same potential energy? No, because it is no longer in the gravitational field of the earth In other words, it is the gravitational field that an object with mass has that gives gravitational potential energy Just like how a gravitational field has gravitational potential energy, an electric field has electric potential energy Consider an object in the gravitational field of the earth Then its potential energy will be given by u equals mgh Where u is the potential energy in joules m is the mass of the object in kilograms g is the gravitational acceleration on earth in meters per second squared and H is the height from which the object is dropped in meters Note that H is how high the object has been dropped in other words displacement So we can replace H with s Now let's say this object was moved to some arbitrary gravitational field Then g the gravitational acceleration of the earth would no longer apply Instead, let's call it the new gravitational acceleration due to this new gravitational field a We know Newton's second law f equals ma so we can write u equals fs Doesn't this equation look familiar? In fact the potential energy u is equivalent to work done w So through some substitutions, we've gone from the potential energy equation to the work displacement equation But we can go further Let's say this potential energy wasn't due to the gravitational field instead due to an electric field Then we know that in an electric field f equals eq Where f is the force an electric field with strength e exerts on a charged particle q So we can write u equals eq s Volts are a measure of electric potential energy in fact the change in volts denoted delta v is equal to e s So now we have u equals delta v q Which tells us that when there is a change in voltage there is work done on the charged particle by the field This equation is often written in the form delta v equals u on q Quite often people also drop the delta So you will often see this equation written as v equals u on q We can do a unit check Voltage has units of joules on coulombs Potential energy has units of joules and Charge has units of coulombs So the units check out