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## Physics library

### Course: Physics library>Unit 11

Lesson 3: Electric potential energy, electric potential, and voltage

# Electric potential at a point in space

Electric potential, a key concept in physics, is an abstract number associated with points in space. It's different from electric potential energy, but related. The units of electric potential are joules per coulomb, hinting at its connection to energy. The video explains how to calculate electric potential and its relationship with voltage. Created by David SantoPietro.

## Want to join the conversation?

• What is electric potential difference? • Is it not true that whether a charged particle gains or loses potential energy between two points in an an electric field depends on what sign the charge has, and what the sign of the charged particle creating the field is? So say we have an electric field created by a positively charged particle, and point A is close to the charged particle creating the field, and point B is further away and the voltage difference is 10 between A and B. A negatively charged particle placed in the field at point A will gain 10 joules per coulumb by moving from A to B (moving it away from where it is 'inclined' to travel to) and it will lose 10 joules per coulomb of potential energy by travelling from B to A. Is this correct?
• how does this (voltage) work in actual electric devices? •  voltage is change in electric potential and when there is change in potential an electric field will be generated which causes the free electrons in the electric devices to move in a specific direction which is opposite to the direction of electric field i.e. from negative to positive direction and thus current is generated by the motion of electrons thus the electric devices work due to voltage.
• why dont we square the distance to find V like in electrostatic force or electric field? • Also, when relating Voltage and work(energy), you find that by taking the equation Voltage = Electric Field * Distance and multiplying the entire equation by Charge to get Work = Electric Field * Distance * Charge and then taking the derivative of this equation (by distance), you get Force = Electric Field * Charge. In other words, this means that the equation you used to get Voltage(kQ/r) will similarly require differentiation and this will lead to the squaring of the distance(kQ1Q2/r^2) that we know as the electrostatic force equation.
• Does a 10V battery have more electric PE than a 1V battery because the difference in electric potential (voltage) b/w the positive and negative charges is greater in the 10V battery? Therefore, the 10V battery has more potential energy to do more work? • An intuitive way to think about potential energy is to consider two water tanks. Tank one has twice as much water in it as tank two so that there exists more potential energy in it than tank two. If a pipe is now connected between the tanks there will exist unequal potential energies resulting in a flow of water from tank one to tank two until the water equalised. Another way to think of it is that tank one has a potential energy level that is 'looking' to find an equilibrium point that it can become equal to. This is what happens in electric circuits where electrons are moved from one point in a circuit that has a higher potential to some other point of a lower potential, thus enabling current flow. Of course, in the above example, if we then connected an outlet pipe from tank two to the ground there would be a further current flow due to the fact that there existed a potential difference between tank two and ground.
• My book (and wiki) says that electric potential is the work done to move a unit charge from infinity to a point in space. But what does that actually mean? What has infinity got to do here? I like the definition which says that EP is a property of an electric field at a certain point in space. It makes sense to me. • Being infinitely far away from other charges just means the electric potential will be zero. If you move towards a positive charge, the potential will increase from 0 to some positive value getting more positive as you get closer to the positive charge. If you move towards a negative charge, the potential will decrease from 0 to some negative value getting more negative as you get closer to the negative charge. So the only place in space where the potential will be 0 is when you are infinitely far away from all charges or the net potential from multiple charges adds up to 0 at a particular location (ex. halfway between a positive and negative charge of the same magnitude).
• so when he says the charge has 200 Joules does he mean that it would take 200 Jouls of energy to move that charge from where it is to the Q charge? • does that mean that at the exact point where the charge is there is a infinite voltage • Its a great question.

Yes, it would seem so huh?? But think about infinite in same way as you think about infinite distance....r. How far away is it? maybe only a few metres or even km at most. so maybe the voltage will also reach a realistic level. Also, remember issues such as
1) this equation is for a charge in isolation. and therefore unrelistic
2) other forces such as the strong force will come into play for some charged particles.

I like the way you are thinking about the situation....what is your response to my few suggestions here?
• If i have two similar metallic spheres having charges +q and -q seperated d cm apart frm each other in vaccum.what is the net electric potential at the midway of the line joining them?   