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. The SI unit of electric potential is the volt. Because the dependence on the charge q has been divided out, the electric potential depends only on position. If a charge q at point P (in electric field E) has electric potential energy U, the electric potential V at that point is: → introducing the electrical potential energy per unit charge, known as electrical potential, which doesn’t depend on known as electrical potential, which doesn’t depend on the amount of charge. the amount of charge. So essentially, potential energy is capacity for doing work which arises from position or configuration.

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 object are placed there, they are at the same potential, but the one with more charge on it has higher electric potential energy

The potential, V, at a point P in an electric field, is the work done per unit of positive charge in order to bring it from infinity to that point. The zero of electrical potential is at infinity. Reformulating definition of electric potential: Following is derivation of potential and potential energy due to a point charge Q The amount of gravitational potential energy depends on the reference point. In contrary, we choose that: The zero of electrical potential and potential energy is at infinity.

q F P at distance r from Q Q q ΔrΔr ΔsΔs F el =k Qq r2r2 W = Fs cosθ To bring positive charge q to point P from infinity (at constant speed), one must apply external force |F| = |F el | to push it against electric field. Work done by that force is positive and is stored as potential energy of charge q at point P. and potential at point P is: Q

Point charge Q - a very confusing picture – time to study! + P E F Q E F Electrical potentials can be positive or negative. _ P E F Q F E

_ F Q F +F Q F V2V2V2V2 V1V1V1V1 V 1 < V 2 Positive charge accelerates from higher potential to lower potential. Positive charge accelerates from higher potential to lower potential. Negative charge accelerates from Negative charge accelerates from lower to higher potential. lower to higher potential. V1V1V1V1 V2V2V2V2 V 1 > V 2

Electrical potentials can be positive or negative. Point charge Q - a very confusing picture – time to study!

Electrical potentials can be positive or negative. V 1 < V 2 Positive charge accelerates from higher potential to lower potential. Positive charge accelerates from higher potential to lower potential. Negative charge accelerates from Negative charge accelerates from lower to higher potential. lower to higher potential. V 1 > V 2

The difference between the potentials at two different points (A & B) measures the work done per unit of positive charge in order to move it from one point to the other. Potential Difference Between Two Points (ΔV = V B – V A ) ΔV = W ΔU = q q

If a charge, q, is moved through a potential difference, ∆V, then the work done on it is equal to the change in its electric potential energy which is converted into kinetic energy:  W  =  U = q  V = ½ mv 2 Law of conservation of energy: change in potential energy = change in kinetic energy Work – kinetic energy theorem work done by net force (electric force) = change in kinetic energy

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

Uniform electric field, E A ball accelerates as it loses potential energy. Similarly, a positive charge accelerates from a region of higher potential toward a region of lower potential. ◊ The change in potential energy of a charge q is converted into kinetic energy: ∆U = q ∆V = ½ mv 2 ∆U = q ∆V = ½ mv 2 ◊he change in kinetic energy is equal to the work done on charge q by el. field: ◊ The change in kinetic energy is equal to the work done on charge q by el. field: Fd = qEd = ½ mv 2 Fd = qEd = ½ mv 2

◊ 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.