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Electric Potential When going for a hike there are two things to consider. Chapter 16 1. How high up are you going? (What is your change in elevation?) 2. How much energy will it take to get there? (How much potential energy will you have once you get there?) Which hiker is doing more work to get to the top of the mountain? (which hiker will have more potential energy when at the top?) Even though they are climbing the same mountain the hiker with the heavier (more massive) load will be doing more work (or will have more potential energy at the top) If the hiker trips, his potential energy will convert into kinetic energy and he will fall down the hill. Just like hikers, charges can have potential energy too. That is called ELECTRIC potential energy. Electric Potential & Electric Potential Energy Work Done on the Ball Energy (Potential) Gained Kinetic Energy Work Done equals Energy Gained Electric potential energy has to do with where the object is (V) (compared to where it wants to be) and how much charge it has (Q). PEE = QV GRAVITATIONAL potential energy has to do with where the hiker is (y) (how high up are they) and how hard gravity pulls on them (mg) (how heavy their pack is). PEg = mgy 1 Electric Potential Energy The sign of the charge in thisamount case matters Defined as the actual of ! energy a charge has as a result of its being acted upon by an electric field. In general, no one really talks about how much work someone did climbing a mountain or how much potential energy they had once they got there. Instead everyone talks about the elevation of the peak. The same is true for charged objects. PEelectric = QV We are usually interested in potential energy difference, or the change of potential energy would be similar to Electric Potential This defining height as the potential energy per unit weight. Defined as the electric potential energy per unit charge. For a point charge, or spherical charge, the potential is given by the formula… V= kQ d Potential has units of energy/charge Joules/Coulomb = Volts Electric Potential describes properties of a point in space as the result of being in the proximity of a charge. Just as height describes properties of a point in space as the result of being in the proximity of a gravitational field. Q A brief Recap: •The electric field describes what an object in the proximity of a charge is feeling regardless of the amount of charge on the object. •The electric potential describes where an object in the proximity of a charge IS compared to where the object wants to be regardless of the amount of charge. •The height describes where an object is in the proximity of another mass compared to where the object wants to be, regardless of the amount of mass. Charges move to decrease their potential ENERGY Masses will always try to move to lower their potential energy. (This is why meatballs roll off the table and onto the floor…) Charges will always move to lower their potential and thus their potential energy. But it gets a bit trickier High PE Low PE +34 J -34 J 2 PE = QV - Positive charges want to be close to -2.3V negative charges +Q x -V = - PE -28.2V 8.8V 1) 1/3 2) 1/9 3) 3 4) 9 5) zero + -9.7V 1.7V If the distance from a negative 3C charge is tripled, the electric potential changes by a factor of… -5.7V Negative charges want to be close to positive charges -Q x +V = - PE If the distance from a negative 3C charge is tripled, the electric potential changes by a factor of… 1) 1/3 2) 1/9 3) 3 4) 9 5) zero You will NOT confuse Electric Potential with Electric Potential Energy! Two point charges of +3.4μC and +6.6 μC (10-6) respectively, are separated by 0.20m. What is the potential energy of this 2 charge system? Another equation for electric potential energy (wait for it…) PEelectric = QV PE = 1) +0.34J 5) +5.2J kQ V= d 2) -0.75J 3) +1.0J 4) -3.4J kQ1Q2 d Q 3 Two point charges of +3.4 and +6.6 microcoulumbs (μC, 10-6) respectively, are separated by 0.20m. What is the potential energy of this 2 charge system? 1) +0.34J 5) +5.2J PE = 2) -0.75J kQ1Q2 d = 3) +1.0J When going hiking, it is helpful to bring a map. Hikers use topographical maps. 4) -3.4J (9 × 109 )(3.4 ×10−6 )(6.6 ×10−6 ) 0.20 PE = 1.01 Joules Electric Potential due to a Point Charge Equipotential Lines & Electric Field Lines + + + + + + + The Electric Potential Produced by a Heart Beat The lamp will not glow when it is held with both ends equidistant from the charged Van de Graaff generator. But when one end is closer to the dome than the other, a current is established and it glows. Why? 4 Consider equal potential lines Consider equal potential lines Consider equal potential lines Hmmm…Now the ends are at a different potential It’s all about the chemicals Hmmm…the ends are at the same potential Why does anyone care about electric potential? Why do they react? All elements strive to have 8 valence electrons. What happens when two chemicals are mixed together? sodium + water = 2 # of Valence electrons 1 2 3 4 5 6 7 8 They React! 5 Some elements do this by giving away valence electrons K -> K+ + eSome elements do this by gaining valance electrons Batteries harness this flow of electrons. In a battery, elements are placed close to each other, without touching, so they do not react. S + 2e- -> S2When a potassium atom (K) is placed next to a sulfur atom (S), they react and electrons flow from the potassium atom to the sulfur atom. A wire connects the two elements. The wire allows the transfer of electrons from one element to the other. This means, there must be an electric potential difference between potassium & sulfur. This movement of electrons generates ELECTRICITY! Rechargeable batteries Rechargeable batteries can be “reset” A dead rechargeable battery can be plugged into the wall. As the zinc (Zn) looses electrons, it goes from solid zinc into an ion dissolved in water. As the dissolved hydrogen ions (H+) gains electrons, they become hydrogen gas and leave the container. Eventually the chemicals run out, and the battery is considered dead. r V E= d The electric potential (voltage) from the WALL returns the electrons and chemicals to their original starting position to be used again. This process is not perfect so rechargeable batteries eventually die as well. Consider two parallel conducting plates. There exists between them a uniform Electric Field. V Actually, the field is uniform only if… 1. You are not near one of the edges. 2. The size of the plates is large compared to the separation. d 6 At which location will the electric field between two charged parallel metal plates be the strongest in magnitude? Consider a positive charge between the plates… 1) Near the positive plate + + + +Force + + + 2) Near the negative plate + 3) Midway between the two plates 4) It’s actually constant throughout the space between the plates. + r- V E= V d F =Q r - - rF = QE r - - + 1 3 2 - d At which location will the electric field between two charged parallel metal plates be the strongest in magnitude? 1) Near the positive plate 2) Near the negative plate + - V 3) Midway between the two plates 4) It’s actually constant throughout the space between the plates. V V + + ++ - --- - ----- + + + + 7 V Electrostatic Equations: Force Electric Field Electric Potential Electric Pot. Energy F unit: N E unit: N/C V unit: V kQ V= d PE unit: J kQ Q F = 12 2 d kQ E= 2 d F = EQ QV F= * d PE = kQ1Q 2 d PE = QV V E= d * PE = QEd * •Parallel plate equations: d = distance between plates 8