# A question on potential

1. Sep 20, 2006

### AlbertEinstein

Well I am not sure where to post this. But, anyway, I am finding 'potential' to be rather difficult. Afterall what is this potential? it comes popping out in different forms such as in potential energy ,potential difference ,electric potential etc.
I also know ,for example, that electric potential is a scalar way of describing the electric field; a system always contains some potential energy, BUT I don't see any need to do this. Electric field can always be described by vectors, then where is the need for potential? Potential energy is also related in the formulation of langrangian which is yet another way of describing classical physics.
Please explain to me that afterall why this potential was invented?

2. Sep 20, 2006

### AK2

Electric fields and other fields like magnetic and gravitational fields , potential and field intensity is used to describe such fields. Potetiental is related to energy just the way field intensity is related to force. Field strength is basically force per unit area. Let me use potential to describe gravitational field.Gravitation potential of the sun is relation to infinity.As work is done to make the body closer to the sun the potential is more negative.This is because an external agent is doing work rather than the gravitational field.

3. Sep 20, 2006

### ZapperZ

Staff Emeritus
One of the clearest way why a potential field is more useful than the electric field is the fact that the electric field is a vector, and that it is more difficult to deal with mathematically. You'll see that when you have a slightly nasty geometry to solve, deal with the electric field is almost impossible to solve. The scalar field tends to be more forgiving. Furthermore, it is easier to get the E field from the V field, rather than the V field from the E field (easier to differentiate than to integrate, to put it crudely).

You can actually convince this yourself. Get a spherically symmetry charge distribution, and don't use Gauss's law. Start from Coulomb's law for the most general form of E-field for a charge distribution, and the most general form of the V-field for a charge distribution, and solve the integral equations for that spherically symmetry charge distribution. You'll realize right away which one is easier to handle.

This is actually nothing unusual. In classical mechanics, one can solve the equation of motion of a system either by using Newton's laws, or Lagrangian/Hamiltonian. Newton's laws deal with forces (vectors), whereas Lagrangian/Hamiltonian deals with energy (scalar). There are many instances, especiallyin complicated systems, where using the Newtonian laws of forces are simply atrocious, but it is solvable using Lagrangian/Hamiltonian.

Zz.

4. Sep 20, 2006

### Andrew Mason

It seems to me that your question is really: why do we talk about energy rather than force? This is not a bad question.

Energy is important because, over time, we have discovered that it is a useful quantity. It is particularly useful in a conservative field, such as electric or gravitational fields, where the energy or ability to do work of a charge/mass depends only upon its position in the field.

Our experience is that energy can be a more useful concept than force. It took centuries for physicists to appreciate its importance. Prior to the 19th century physicists talked about the vis viva of an object. See:http://en.wikipedia.org/wiki/Conservation_of_energy#Historical_development". The usefulness of energy became apparent with the introduction of steam engines. It was realized that while forces could be easily manipulated (eg by changing piston size) the ability of the engine to do something useful depended on energy - the product of force and the distance over which it is applied - rather than just the magnitude of the force it could produce.

AM

Last edited by a moderator: Apr 22, 2017