# What is the Potential Difference VC-VA?

When the terminals of an electric battery are connected is when sparks and heat arise.

These phenomena show that battery energy is being transformed into light, sound, and heat energy.

The battery itself is converting chemical energy into electrical energy.

This, in turn, is transformed into other forms of energy (such as heat) in the conductors that connect the terminals.

But to understand what voltage is we need another very simple concept, that of change in potential energy.

Formally its definition equates it with the work we need to move a frictionless object from one point to another.

### For example:

The potential energy of a book on a shelf is greater than that of the same book on the floor.

This increase in potential energy is due to the fact that we need to do work to put the book on the shelf overcoming gravity.

We can easily understand that this difference in potential energy will depend on three factors: the mass of the book, the magnitude of the force of the gravitational field.

And the difference in height between the ground and the bookshelf.

Similarly, electric potential energy changes when work is done to move an electric charge from one point to another within an electric field.

This change (symbolized by the Greek letter delta, Δ) in potential energy, Ep.

It is likewise the work done. The magnitude of this change in potential energy depends on how large the charge is, q, as in the case of the book it depended on the mass of the book.

If we divide the change in potential energy, ΔEp, by the charge we move, q, we get a value that does not depend on how large or small q is.

Instead, it will depend solely on the intensity of the electric field and the location of the start and endpoints.

This value is called the electric potential difference and is precisely defined as the ratio between the change in potential energy, ΔEp, of the charge q and the magnitude of this charge. Using symbols:

### V = ΔEp / q

The unit of the potential difference corresponds to the energy divided by charge, or joules per coulomb.

As this is very cumbersome, the unit is given a name of its own, again in honor of Volta.

### Its symbol is “V”.

The difference in electric potential (or voltage) between two points is one volt (1 V) if one joule (1 J) of work is done by moving a coulomb (1 C) of charge from one point to another.

The work done to carry the charge q from A to B does not depend on the path taken.

The potential difference between two points in a continuous electric field depends on the location of the points and not on something else.

It does not depend on the path that the load has followed to get from one point to another.

It doesn’t matter whether the road is long or short, straight or twisted, the same work is done per unit load.

A mountaineer does the same work against the gravitational field per kilogram of the mass of his backpack.

When he climbs it in a straight line from the base to the top as when he follows a winding path that progressively ascends the mountain.

The case of the potential difference between two points in an electric field is similar.

## What potential difference is needed to accelerate a? Electric potential energy, like gravitational potential energy, can be converted into kinetic energy.

A particle charged in an electric field, on which no other forces act, will accelerate.

By doing so, you will increase your kinetic energy at the expense of potential energy.

In other words, the electric force on the active charge in such a way that it pushes it to regions of the field of lower electric potential.

A charge q that falls by a potential difference V increases its kinetic energy by a value qV if it does not lose anything by friction. Symbolically: ΔEc = qV.

The increase in kinetic energy is equal to the decrease in potential energy.

Therefore, the sum of the two energies at any moment is constant.

This is just a particular case of the general principle of conservation of energy, even though only electrical forces are acting.

The conversion of electrical potential energy into kinetic energy is used in electron accelerators.

There was a time, very recently, when there was at least one in every home: televisions and picture tube monitors.

## What potential difference did the proton move through? When an electron with a charge of 1.6 · 10-19 C moves through a potential difference of 1 V, its kinetic energy increases by 1.6

10-19 J, since ΔEc = qV. This amount of electricity is called the electron volt and is abbreviated eV.

Its multiples are, for example, the kiloelectron-volt, 1 keV (one thousand eV), the megaelectron-volt, 1 MeV (1 million eV) or the gigaelectron-volt, 1 GeV (one billion eV).

The energies of the particles in accelerators are usually expressed in these multiples. In a television tube, the beam is accelerated with a potential difference of about 25,000 V.

So, each electron has an energy of 25 keV.

In an electron microscope, we speak of energies of the order of 200 keV. In the most common particle accelerators, the energies range from 800 to 1000 GeV. The

LHC (Large Hadron Collider) is currently designed so that the particles in each beam reach energies of 6.5 TeV, teraelectron-volts, or 6.5 trillion electron-volts.

The potential difference between points A and B, VB − VA, is thus defined to be the change in potential energy of a charge moved from A to B, divided by the charge.

Units of potential difference are joules per coulomb, given the name volt (V) after Alessandro Volta.