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Voltage Notes March 15-18

Today • Questions re: HW • New Concept: Electrical Potential , EPE (J; eV) • /Voltage, V (V) > Near a point charge Q > Between two Parallel Plates

Honors Physics 1 Voltage Notes March 15-18

Electrical Potential Energy, EPE (J) When two charges Q and q are separated by a distance R, there is a certain amount of potential energy stored in that configuration (similar to energy stored in a spring, or the potential energy between two masses).

Q R q

We say that, in this case, where k = 9 E9 Nm2/C2. By definition, the EPE between these two charges is defined to be zero when R = ∞. Notice that, when Q and q have the same sign, then EPE is positive; when Q and q have opposite signs, then EPE is negative. *This implies that, when EPE is positive, the charges want to move away from each other; when EPE is negative, the charges want to come together. Technically, the EPE stored in this system is defined as the done by an External Force AGAINST the Electrostatic Force in bringing these two charges together from an infinite distance away. *If there are more than two charges, you can compute the Total EPE of a system by determining the EPE for each possible pair of charges, and then summing the EPE's. E.g., for 3 charges...

Honors Physics 2 Voltage Notes March 15-18

Electric Potential/Voltage, V (V) We define Electric Potential, aka Voltage, as the EPE per unit charge; i.e., we define V as the ratio of EPE a charge has at a certain point to the amount of charge itself (this is similar to how we define E as the ratio of Force per unit charge). The key idea is that V relates to ENERGY.

Q R q For the case on the previous slide, the Voltage at the location of charge q, which is a distance R from the charge Q, would be

The idea is that, when I place a charge q at a point in space where there is a Voltage V, that charge will then have an EPE = qV. *Notice that the V at the location of q is INDEPENDENT of the charge q. If Q is positive, then the Voltage would be positive; if Q is negative, the Voltage would be negative. (This tells us simply that if we place a positive charge q at this point, EPE is positive, and if q is negative, then EPE is negative.)

Honors Physics 3 Voltage Notes March 15-18 Batteries: When you look at a battery (for example, a AAA in your calculator), it is labeled as "1.5 V". This implies that the DIFFERENCE in Voltage between the two terminals is 1.5 V; in turn, this means that the amount of energy that a charge (say, an ) will gain in moving through the battery is EPE = qV = 1.6 E-19(1.5) = 2.4 E-19 J. There is another unit of energy that is often used when discussing : the Electron-. 1 eV = 1.6 E-19 J; it is the amount of energy that a proton/electron will gain when it moves through a voltage of 1 V. Thus, in the above example, the would have an energy of 1.5 eV.

Honors Physics 4 Voltage Notes March 15-18

Example 1: What is the Electric Potential a distance of 0.25 m from a if it has a net charge of -8 E-6 C?

Example 2: A carbon nucleus has 6 protons and 6 neutrons. What is the Voltage a distance of 3 E-12 m from this nucleus?

*Example 3: What is the Electric Potential difference between points A

and B (∆V = VA - VB) in the diagram below? Assume Q = 4 E-6 C. 1 m 3 m

Q A B

Honors Physics 5 Voltage Notes March 15-18

Relationship between V and E: In a region where the is Uniform, if a charge q moves over a distance d, it will experience a change in Electric Potential such that

*We must understand going forward that it is only the difference in Voltage that matters as far as charges are concerned (similar to how only changes in potential energy are truly meaningful). Often we will choose either our "initial" or "final" Voltage as zero, and hence we will often conclude that V = Ed

In the diagram to the left, assume there is a uniform Electric Field E that is directed downwards, and the distance from top to bottom is d. A charge +q placed near the top "plate" will feel a force directed downwards; its EPE at that point would be positive, and it would have a The Voltage "difference" tendency to move downwards. between the top and the bottom, V = Ed. By the definition of V, this V = EPE/q; in other words, the EPE = qV = qEd. Compare this to the following: In the diagram to the right, a mass m is placed in a uniform gravitational field g that is directed downwards. When released from rest, the mass feels a force directed

downwards; its PEg at this point would be The difference in potential positive, and as a result it would have a energy from the top to the

tendency to move downwards. bottom is ∆PEg = mgh.

Honors Physics 6 Voltage Notes March 15-18

Honors Physics 7