# Irrelevance of electrical potential

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1. Mar 5, 2017

### Luke0034

In regards to voltage and electrical potential, I have a question.

I understand the voltage to be the difference in electrical potential of two separate points. So in an analogy am I correct to compare this to a bowling ball being 4 feet off the ground. So the bowling ball has a gravitational potential at 4 feet, and a gravitational potential at zero feet (the ground). Now my question is, is a single point of electrical potential useful at all without a second point for reference? For example, if the electrical potential at one point is 200 J/C, then does that mean anything without a point of reference to the 200 J/C? The same as the bowling ball would have no meaning without reference to the ground? So does a single point tell us anything about how a charge will behave at a point, or do you need the difference between points to tell how it will behave. I am thinking you need both points, because a bowling ball 4 feet high essentially can't "mean" 4 feet high without a reference point to 0 feet. So how can electrical potential at one point even be measured without having a reference to something else. That is how can V = kq/r be an equation that tells anything when it doesn't have a reference point. What does "electric potential" a single point refer too (not voltage the difference between two points)?

2. Mar 5, 2017

### tech99

For an isolated charged object, there is a potential between it and the rest of the Universe. The potential is the work done in bringing a unit charge to the object from an infinite distance.
Taking the discussion a little further, it is interesting that if we have two plates spaced apart by a few times their maximum dimension, then the capacitance between them is roughly that for two isolated objects in series, and is much greater than that calculated for a parallel plate capacitor.

3. Mar 5, 2017

### SlowThinker

As tech99 says, you can take a reference point at infinite distance.
But this is a general feature of any potential: if you add a constant to it, all measurable results stay the same.

4. Mar 5, 2017

### Luke0034

Thank you for the answer, I think I understand. So would I be correct to say that if the electrical potential at a certain point was 200 J/C, then that means that it would take 200 J of energy to move a 1 C charge from infinity to that point? But in terms of a circuit, the electrical potential at one point, that can still be thought of bringing a charge from infinity meters away in the universe all the way to that point in the circuit? I'm guessing the strength of the electrical potential at a certain point is dependent on the strength of the electric field there? Could you please explain the relationship between the electric field and electrical potential? Again thank you, that helps a lot.

5. Mar 5, 2017

### Luke0034

Can you explain what you mean by "add a constant to it." Maybe an example would help me understand what you're saying. Thanks.

6. Mar 5, 2017

### SlowThinker

I don't know how much math you have done, and I'm probably not the best person to explain things, but...
For example, the force exerted by gravity on an item of mass $m$ is $F=-m\frac{\Delta\Phi}{\Delta h}$ (generally only for small $\Delta h$). For example at height 20 meters the gravitational potential can be $9.8{\times}20 \text{ J/kg}$. At height 23 meters the potential is then $9.8{\times}23\text{ J/kg}$. Thus the force on an item of mass 2 kg is $$F=-2\times\frac{9.8\times23-9.8\times20}{23-20}\text{ J/m}=-2\times9.8\text{ N}$$
Now if the potential at 20 meters was $9.8\times20+12345\text{ J/kg}$ and at 23 meters it was $9.8\times23+12345\text{ J/kg}$, the force would stay the same. This is how all potentials work. You can add a constant to it, and the numbers change, but the measurable results (forces, acceleration, energy used) stay the same.
You can pick any constant you like. Sometimes it's such that objects at sea level have zero potential, other times objects at your table have zero potential, other times it's objects at infinity that have zero potential. Once you pick a reference point, all other values are determined.
Again, this is a feature of every potential, not just electric or gravitational potential.

Electric field between 2 points is given by the difference of potential between the 2 points (if the path between them is clear). Same as before: the field is the same, whether one point has $\text{2 J/C}$ and the other has $\text{1 J/C}$, or one has $\text{2+34567 J/C}$ and the other has $\text{1+34567 J/C}$. The movement of electrons is the same in both cases.