Two different things that sound alike! Electrical Energy and Electrical Potential In order to bring two like charges together work must be done. In order to bring two like charges together work must be done. In order to separate two opposite charges, work must be done. Recall Work: W = F d cos(  ) As the monkey does + work on the positive charge against electric force, he increases the energy of that charge. The closer he brings it, the more electrical potential energy it has. Try the same thing with grav. force. It is the same!!!! charge → mass This work done by external force against electrical force is stored as electrical PE, U. When he let it go, the charge will gain kinetic energy and can do a work.

Greater amount of charge → greater force needed → greater work done → greater stored potential energy U. So essentially, electrical potential energy of a charge is its capacity to do the work due to its position within electric field. In the electrical case, a charge placed in electric field will have electric potential energy. How do we know that? If left on its own it will start accelerating due to electric force acting on it. We say it has electric potential energy which will be converted into kinetic energy. On the other hand if external force pushes the charge against electric field, the work done by that force will be stored as potential energy in the charge. As we saw potential energy depends on the amount of charge, like the force is dependent on the amount of charge. So the same idea that led us to introduce electric field will lead us now to introduce ELECTRIC POTENTIAL.  U = W

Potential Difference Between Two Points (ΔV = V B – V A ) per unit positive charge is equal to the work done per unit positive charge in order to move it from one point to the other. ΔV = W ΔU = q q Now the same way as before with electric field, potential difference does not depend on the charge. Note important difference between energy and potential: Note important difference between energy and potential: A point has potential, charge placed there has electric potential energy A point has potential, charge placed there has electric potential energy Two points that are at the same distance from the charged object have the same potential So, when two charged objects are placed there, they are at the same potential, but the one with more charge on it has higher electric potential energy. It is harder to push it there

Capacitor: two parallel conducting plates charged uniformly with opposite charge uniform electric field constant magnitude and direction uniform electric field (the one that has constant magnitude and direction) is generated between two oppositely charged parallel plates. Edge effect is minimized when the length is long compared to their separation. ▪ Positive charge accelerates from higher to lower potential (from positive to negative). ▪ Negative charge accelerates from lower to higher potential. (from negative to positive)

A ball in gravitational field accelerates. It loses potential energy and gains kinetic energy. ◊ ◊ The work done by gravitational force is equal to the decrease in its gravitational potential energy which is converted into kinetic energy W grav = Δ PE = ΔKE W grav = Δ PE = ΔKE Work done by electric force on charge q ▪ Work done by electric force on charge q W = ∆U = ½ mv 2 q ∆V = ½ mv 2 W = Fd = q Ed

A ball in gravitational field is pushed up by external/applied force against gravitational field. ◊ ◊ The work done by applied force is stored as change in gravitational potential energy in the object. Work done by external force on charge q ▪ Work done by external force on charge q W ext = Δ PE

electron-Volt (eV) The electron volt is not a smaller unit for volts!!! The electron volt is not a smaller unit for volts!!! It is a smaller unit for energy. It is a smaller unit for energy. How much work is done in moving one electron through a potential difference of one volt? An electron volt is the amount of energy/work it takes to move an electron through a potential difference of 1 volt. 1 eV = 1.6x J 1 eV  U = W = (1.6x C) (1V)  U = W = q  V

◊ relationship between uniform electric field E and potential difference between two points distance d from each other along electric field line: ΔV = Ed → E = ΔV/d and NC -1 = Vm -1 ΔV = Ed → E = ΔV/d and NC -1 = Vm -1

For things like batteries, we specify the potential difference between the contacts (poles) on the batery. So a "D-cell" has a rating of 1.5 volts which means that every 1C of charge (electrons) that moves from the negative side of the cell to the positive side will do 1.5 Joules work. 1. Potential difference = 1.5 V → 2. Potential energy of 1 C electrons relative to positive pole is 1.5 J. pole is 1.5 J. 3. That energy is being converted into kinetic energy on the way to positive pole. the way to positive pole. 4. Kinetic energy is being converted into work due to collisions with atoms within conductor. That is what collisions with atoms within conductor. That is what makes bulb (and wires unfortunately too) to heat up makes bulb (and wires unfortunately too) to heat up and give off light (not wires, hopefuly) and give off light (not wires, hopefuly) 5. Electrons reach positive pole completely exausted without any energy, ready to reenergize again in the cell. any energy, ready to reenergize again in the cell. The AA-cell may only light a light bulb for 15 minutes while the D-cell may keep the same bulb lit for several hours (simply more charge). The AA-cell may only light a light bulb for 15 minutes while the D-cell may keep the same bulb lit for several hours (simply more charge). In the 12 volt car battery, every coulomb of charge that moves from one side to the other does 12 Joules worth of work. In the 12 volt car battery, every coulomb of charge that moves from one side to the other does 12 Joules worth of work. In a 120 volt electrical outlet, every Coulomb of charge does 120 Joules worth of work as it moves from one side of the outlet to the other.

surprise, surprise ! We use the same name for different things, and even worse we use couple of different names to express the same thing, like: 1.The variable we use for potential, potential difference, and the unit for potential difference (volts) is V. Cute!!!!! 1.The variable we use for potential, potential difference, and the unit for potential difference (volts) is V. Cute!!!!! 2.Don't let that confuse you when you see V = 1.5V 3.Electric potential energy is not the same as electrical potential. 4.The electron volt is not a smaller unit of the volt, it's a smaller unit of the Joule. 5.Electrical potential can also be described by the terms, potential difference, voltage, potential drop, potential rise, electromotive force, and EMF. These terms may differ slightly in meaning depending on the situation.