# I Clarification between electric field and potential energy

1. May 21, 2017

### Notaphysicsmajor

From my understand, electric field is the force emitting from a charge. This means that if a charge was placed in the vicinity of the charge that was emitting the field of force, that charge placed would experience a force from it. How does potential energy differ from this? I understand that potential energy is in joules, meaning it's work. So does that mean it's the amount of work being done on the charge? Say there is a positive charge there and a negative charged was placed x distance away from it. Would calculating the potential energy from that distance be the amount of work done to bring the two charges together? In this example it would be the positive charge moving towards the negative charge? What would happen if it was two of the same charges in that it would experience an repulsive force, say two positive charges?

In a battery, the amount of volts it provides is the amount of work per coulomb? So it would be providing 1.5 joules per 6.24*10^8 electrons?

2. May 21, 2017

### sophiecentaur

The difference is enormous, although, at first sight, they appear the same.
Field produces a Force on an object. Potential is the Energy needed to get that object from a start position to a final position. That applies to electricity and magnetism and also to Gravity. If the force is constant with distance, the potential is F X distance moved.
Work and Energy are really what counts in life. Force is of rather 'secondary' importance. Voltage (correct term: Potential Difference) tells you the energy available when a charge moves through a Load (heater / light bulb / motor). Potential (Energy) is Force times distanced moved in the direction of the force. It's easier to start off with a charge between two wide plates with V volts across them (the maths is simpler because the Field is uniform). The field (E) between the plates, spaced by d, is V/d and it's units are Volts per metre. The potential (work W done moving between the plates will be
Force X distance
which is E X q X d
but E is V/d so Work done is
W = qV
The distance cancels out in those steps which shown that the Work done is independent of the spacing so you can have a whole range of fields for the same work done.
Right idea but the charge on an electron is 1.6^-19C. You will read this message a lot on PF: Electrical Engineering and basic Electrical theory has no need to consider electrons at all. We deal with 'Charge' and we use a unit that's a sensible size (1 A flowing for 1s = 1 Joule). Avoiding electrons helps to avoid trying to give them some sort of mechanical properties like significant Kinetic Energy (which they don't when travelling through a wire).

3. May 21, 2017

### cosmik debris

A potential is a field and you can only measure differences in the field not absolute values at each point. The rate of change of these differences or the first derivative of the potential is the force.

Cheers

4. May 21, 2017

### sophiecentaur

Electric Potential is NOT Electric Field. They are both defined precisely and they have different units so it is nonsense to say they are the same thing. You can measure Field in one point with a charge and a spring balance. The Field is the gradient of the Potential - "rate of change" implies a variation in time and this has nothing to do with time.
What is the point of leaping into a post with ideas that any text book could put you right on.

5. May 21, 2017

### cosmik debris

Yes, my apologies, I don't know what I was thinking.