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Electric Potential Energy | 9 mins | 0 completed | Learn Summary |

Electric Potential | 27 mins | 0 completed | Learn Summary |

Work From Electric Force | 19 mins | 0 completed | Learn |

Relationships Between Force, Field, Energy, Potential | 24 mins | 0 completed | Learn |

The ElectronVolt | 4 mins | 0 completed | Learn |

Equipotential Surfaces | 8 mins | 0 completed | Learn |

Concept #1: Relationships Between Force, Field, Energy, Potential

**Transcript**

Hey guys. In this video we're going to talk about the relationships between the electric force, the electric field, the potential energy and the potential, let's get to it. So far in electricity, we really see four major things, the electric force the electric field, the electric potential energy and the electric potential, these four things all have cellular names and equations. So, you sort of want to break it down on the following table for you guys, okay? We want to sort of put everything together and see how these different things fit together, Alright? So this table is broken up by two things some of these equations are 1 over r squared and some of these equations are 1 over r, likewise some these equations have two q's and some of these equations only have one q, okay? I'm going to get out of the way so you can see the last entry in this table.

So, right here, the first thing we have, which has two q's and r squared, is the electric force, okay? Coulomb's law, we've seen this before K, q1, q2 over r squared, if we stick with q1, q 2 but we do 1 over r, we have the electric potential energy which is K, q1, q2 over r, okay? Moving down the table, if we stick with r squared but we talk about one q, we have the electric field, okay? Which, we've said is best thought about as an electric force field, a field that tells us something about the force, okay? And that's k, q over r squared. Alright, and lastly, if we're talking about one q and r, we have the electric potential, okay? We often call this just the potential, and this is best thought about as an electric energy field, it's a field that tells you information about the energy, okay? Now, we know how to relate top to bottom, we know that the electric field is what produces the force as f equals q, E, if you place a charge q in an electric field E you feel some force, likewise, we can relate top to bottom by saying that the potential is what produces the potential energy and that u equals q, V, okay? We can also relate the right column to the left column, U is related to the electric force by saying Delta U is F, Delta x, okay? This is basically saying that the work, sorry, I'm missing a negative sign here, the work is F, Delta x. Well, work is also negative Delta u, if you guys remember, once again, we can relate the right to left column by saying that the change in potential Delta V equals negative E, Delta x, okay? So, this is a great table that breaks down these four fundamental qualities and their relationship amongst each other, okay? The only two things that don't have a relationship here are the electric force and the electric potential, there's nothing that goes diagonally across the table, likewise for the potential energy and the electric field.

A couple things that are missing from this table is the potential difference and the difference in potential energy, okay? Remember, that the potential difference, right? Which, we also call the electric potential difference, but we can just drop the word electric, is what we refer to as a voltage and it's a Delta V, okay? Likewise, we also have Delta U, don't forget that Delta U, at least the negative of it, is work, okay? So, both of these Delta's, both of these differences have special names, the potential difference is called voltage and the potential energy difference, at least the negative of it, is what we call work, okay? So, this is a great page, you guys should print out this page, you should, you guys should write in the relationships that I included above and this should be something that you refer to when you need to refresh yourself on what these things are and what a relationships between each of them is, alright? Thanks for watching.

Example #1: Potential at Center of Charges in a Square

**Transcript**

Hey guys. Let's do an example with electric potential. What is the potential at the center of the arrangement shown in the following figure. So, we have these four charges put on this square of size 5 millimeters and we want to know the potential at the center, what is V, okay? So, we know that V2 to any point charges k, q, over r and the total potential to Center is just going to be the sum of the four individual potentials of each of those four charges, the question is because, we know they q's, how far are they each from the center, that's the only thing we need to know something, that's important to know about the triangles that we're drawing here, right? We have a triangle with some side lengths 5 millimeters and 5 millimeters is that any triangle where both sides are the same, we can say hypotenuse is it the square root of a squared plus a squared which is the square root of 2a squared which is the square root of two times a, we can pull that a squared out of the square root, so this is going to be the square root of 2 times 5 millimeters which is about 7 millimeters, okay? So, you should these lengths is going to be 7 millimeters. So, now we can calculate each of the individual potentials, let's start with the 2 Coulomb, the two nanocoulomb charge which we'll call v1, right? That's going to be 8.99 times 10 to the 9, nano, don't forget, is 10 to the negative 9, that distance is 0.007, right? Double-oh-seven, meters and this is about 2569 volts. So, that's one voltage down, three more to go, sometimes these problems can be pretty calculation intense but don't worry, it's just tedious, it's not difficult, the next one will say, sorry, v2 will say it's due the negative 3 nanocoulomb charge. Alright, I'm going counterclockwise on this configuration, don't forget the negative sign, negative 3 nanocoulombs divided by 0.007, it's going to be negative 3853 volts, okay? Once again, I hate writing all this stuff, you guys probably hate writing this stuff at this point also, 1 nanocoulomb divided by 0.007, this is going to be once again positive 1284 volts and finally, let me minimize myself, 8.99 times 10 to the 9, we should have a button that just stamped that, negative 1.5 times 10 to the negative 9 divided by the distance, which is once again, 0.007, this whole thing becomes negative 1926 volts, okay? There are the four voltages there done. Now, the total voltage at the center is going to be the sum of these four voltages, okay? Let me minimize myself again, that total voltage, the total potential, sorry, not voltage, potential, is V1 plus V2 plus V3 plus V4, which is 2569 minus 3853 plus 1284 minus 1926 equals positive, sorry, negative, my bad 1926 volts, okay? Thanks for watching, I hope this helped.

Practice: 4 identical charges are arranged so that they are evenly spaced in a circle. If the radius of the circle is 10 cm, and the potential at the center of the circle is – 100 V, what is the magnitude of each charge?

Example #2: Potential Difference due to Point Charge

**Transcript**

Hey guys. I hope you're able to solve this problem on your own, if not here's a little bit of help. A negative 2 Coulomb charge lies at rest, what is the potential difference between point A, which is 1 and a half meters from the charge and point B which is 4 meters from the charge, what would the work on 4 Coulomb charge be it moved from A to B, okay? So, first we want to know the potential difference between A and B which means, we know, we need to know the potential at A and the potential at B, due to a point charge the potential is always k, q over r. So, at A, that's just 8.99 times 10 to the 9, it's a negative 2 Coulomb charge and the distance to A is one-and-a-half meters. So, this whole thing is negative 30,000 volts approximately, V at B is still k, q, over r, which is 8.99 times 10 to the 9, still a negative 2 Coulomb charge but now the distances 4 meters, okay? And this works out to be about negative 11,000 volts. So, the potential difference from A to B is going to be the final potential which is B minus the initial potential which is A, and that's just negative 11,000 volts minus negative 30,000 volts which is negative 11 plus 30,000, right? Those two negatives become plus. So, that's about 19,000 volts, that's the potential difference one problem answered, what about the next problem what's the work done to move from point A to point B for a 4 Coulomb charge? Well, the work did at any potential difference is always negative q Delta V so the work from A to B is going to be negative 2 Delta V from A to B. So, it's going to be negative and it's a positive 4 Coulomb charge times 19,000 thousand volts which is about negative 76,000, okay? So, that is the work to move from point A to point B. Alright, thanks for watching, I hope this helped.

Example #3: Potential Difference Between Two Charges

**Transcript**

Hey guys. Let's do another example about work. A 5 nano Coulomb charge and a negative 3 nano Coulomb charge lie on a line separated by 6 millimeters, what is the potential halfway between the two charges on the line connecting them? What is the potential halfway between the charges but 4 millimeters above the line connecting them? How much work would it take to move a 1 nano Coulomb charge from the first point to the second, okay? So, first let's draw a picture, what's going on with this problem? Well, we have a 5 nano Coulomb charge and a negative 30 nano Coulomb charge separated by 6 millimeters, halfway between them, which we want to find the potential at, is going to be about, sorry, it's going to be 3 millimeters away from each of them, next we want to find the potential at a point halfway between them but 4 millimeters above the line connecting them, okay? That's you, to find the potential at each of these two points we have to know the potential due to both charges at that point and add them together. So, let's start at the point half in between them, I'll say that due to the five nanocoulomb charge at Point A, we'll call this point A, and point B, the potential is going to be k, q over r, right? The potential to get any point Charge, that's going to be 8.99 times 10 to the 9, q for the 5 nanocoulomb charge is 5 times 10 to the negative 9, right? Nano is 10 to the negative 9, and that distance is 3 millimeters, so this is going to work out. So, 1.5 times 10 to the 6 volts, okay? That's one down, three to go, due to the 3 nano Coulomb charge at A, still the same equation, this is 8.99 times 10 to the nine. Now, it's a negative three times 10 to the negative 9 Coulomb charge, don't forget the negative sign, distance is still three millimeters, this is going to be negative 9 times 10 to the 6 volts, sorry, by the way, this is not 1.5 times 10 to the 6, it was 1.5 times 10 to the 7, it's 15 times 10 to the 6, okay? sorry about that guys, so the total potential at A is just going to be the sum of these two, which is going to be 15 times 10 to the 6 minus 9 times 10 to the 6, which is 6 times 10 to the 6 volts. So, that's one down, we have to find the potential at point B now. So, due to the 5 Coulomb charge at B, we have 8.99 times 10 to the 9 times 5 times 10 to the negative 9 divided by, what's the distance now between these charges and point B? Well, let's just look, right? This is going to be this distance, okay? Well, these are just three, four, five, triangles. So, these are going to be 5 millimeters, okay? So, now we know that distance, 5 millimeters or 0.005 meters so this is going to equal 9 times 10 to the 6 volts, finally due to the 3 Coulomb charge, sorry, for the nanocoulomb charge at B, we have 8.99 times 10 to the 9, negative 3 nanocoulombs, don't forget the negative sign, and the distance is once again 5 millimeters, okay? Plugging all the same, we get negative 5.4 times 10 to the 6 volts, okay? So, the voltage at, sorry, the potential at B, which is going to be the sum once again of these two, is going to be 9 times 10 to the 6 minus 5.4 times 10 to the 6 and that's going to be is 3.6 times 10 to the 6 volts. So, now we know those two potentials at the two different points, what is the difference in potential? The potential difference between those two points? Well, to go from A to B, where B is our final point, this is going to be VB minus VA, which is 3.6 times 10 to the 6 minus 9, sorry, not 9, 6 times 10 to the 6, that's going to be negative 2.4 times 10 to the 6 volts, okay? That's one answer down what's the potential difference? Negative 2.4 times 10 to the 6, lastly what's the work done? Well, the work did any potential difference is negative q Delta V, but what's our q? okay? We are told all the way back up here, in the problem, we want to move in 1 nanocoulomb charge from point A to point B. So, q is one nanocoulomb so this is negative 1 nanocoulomb 10 to the negative 9, don't forget, times negative 2.4 times 10 to the 6 and this whole thing works out to be positive 0.0024 joules, okay? That's it, thanks for watching.

Practice: A 5 g, 3 µC point charge is moving with an initial speed of 20 m/s away from a –5 µC charge. If they are initially 5 cm apart, how far can the 3 µC travel before stopping?

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Concept #1: Relationships Between Force, Field, Energy, Pote...

Example #1: Potential at Center of Charges in a Square

Practice #1: Potential at Center of Charges in a Circle

Example #2: Potential Difference due to Point Charge

Example #3: Potential Difference Between Two Charges

Practice #2: Distance to Stop a Point Charge

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