1 00:00:01,300 --> 00:00:04,566 - Let's talk about Electric Potential V. 2 00:00:04,566 --> 00:00:06,266 This is confusing, this is one of, 3 00:00:06,266 --> 00:00:09,633 if not the most confusing ideas in all of physics. 4 00:00:09,633 --> 00:00:13,700 For one it sounds just like Electric Potential energy 5 00:00:13,700 --> 00:00:15,366 but it's not, this is different, 6 00:00:15,366 --> 00:00:18,200 it's related to Electric Potential energy 7 00:00:18,200 --> 00:00:21,200 but the Electric Potential V is different 8 00:00:21,200 --> 00:00:22,800 from Electric Potential energy. 9 00:00:22,800 --> 00:00:24,433 That was a poor choice of naming. 10 00:00:24,433 --> 00:00:26,067 And the other reason it's confusing 11 00:00:26,067 --> 00:00:30,533 is that Electric Potential V is a number, just a number, 12 00:00:30,533 --> 00:00:33,833 that's it, associated with points in space. 13 00:00:33,833 --> 00:00:36,433 So it's abstract, this is an abstract idea, 14 00:00:36,433 --> 00:00:40,733 you can't go hold Electric Potential in your hand, 15 00:00:40,733 --> 00:00:44,966 it's a number, an abstract number at every point in space. 16 00:00:44,966 --> 00:00:46,366 Here is points in space, 17 00:00:46,366 --> 00:00:48,733 I just put circles around empty spots on the screen, 18 00:00:48,733 --> 00:00:50,233 there's like nothing here, 19 00:00:50,233 --> 00:00:50,933 I just put circles here, 20 00:00:50,933 --> 00:00:53,633 these are circles around empty points in space, 21 00:00:53,633 --> 00:00:56,366 just so we can talk about them explicitly. 22 00:00:56,366 --> 00:00:59,200 And, well, if there was no charge around, 23 00:00:59,200 --> 00:01:01,833 if you literally had an empty universe, 24 00:01:01,833 --> 00:01:04,033 the V value at every point 25 00:01:04,033 --> 00:01:06,166 in this universe would be zero. 26 00:01:06,166 --> 00:01:08,200 It'd be zero there, it'd be zero over here, 27 00:01:08,200 --> 00:01:10,366 the number associated with 28 00:01:10,366 --> 00:01:12,233 every point in space would be zero. 29 00:01:12,233 --> 00:01:14,133 That'd be boring, and useless. 30 00:01:14,133 --> 00:01:16,833 How do we make it so that the V value, 31 00:01:16,833 --> 00:01:20,600 the Electric Potential value, is not zero? 32 00:01:20,600 --> 00:01:22,367 We just stick a charge in here, 33 00:01:22,367 --> 00:01:25,766 just stick a big ol' positive Q 34 00:01:25,766 --> 00:01:27,933 at some point in space over here, 35 00:01:27,933 --> 00:01:29,766 take a big ol' charge and we'll stick it right there. 36 00:01:29,766 --> 00:01:32,866 Now, points in space around this charge 37 00:01:32,866 --> 00:01:35,233 will have a V value that's non-zero, 38 00:01:35,233 --> 00:01:38,300 and they'll be big if you're near this Q, 39 00:01:38,300 --> 00:01:41,266 so the V values around here are gonna be really big, 40 00:01:41,266 --> 00:01:43,633 and then the V values way out here will be smaller, 41 00:01:43,633 --> 00:01:46,833 the further way you go the smaller it gets. 42 00:01:46,833 --> 00:01:48,500 And why do we care? 43 00:01:48,500 --> 00:01:49,466 Who cares? 44 00:01:49,466 --> 00:01:51,200 The reason we care is this. 45 00:01:51,200 --> 00:01:55,000 The units of Electric Potential are Joules per Coulomb, 46 00:01:55,000 --> 00:01:59,600 so Electric Potential has units of Joules per Coulomb, 47 00:01:59,600 --> 00:02:01,665 that gives you a hint of why you should care, 48 00:02:01,665 --> 00:02:04,500 we care about Joules, Joules are energy 49 00:02:04,500 --> 00:02:06,433 so something about energy, that's useful, 50 00:02:06,433 --> 00:02:08,032 you can get work out of that 51 00:02:08,032 --> 00:02:10,132 or can turn it to Kinetic energy. 52 00:02:10,133 --> 00:02:13,600 And Joules per Coulomb, that let's you know, 53 00:02:13,600 --> 00:02:16,800 alright, well, if this point over here 54 00:02:16,800 --> 00:02:21,800 happened to have, say 100 Joules per Coulomb, 55 00:02:23,000 --> 00:02:27,333 let's say the V value at this point in space 56 00:02:27,333 --> 00:02:30,066 happened to be 100 Joules per Coulomb, 57 00:02:30,066 --> 00:02:31,433 what that means is, 58 00:02:31,433 --> 00:02:33,233 remember there's nothing there, 59 00:02:33,233 --> 00:02:35,300 but if there was something there, 60 00:02:35,300 --> 00:02:37,200 if we happened to take, 61 00:02:37,200 --> 00:02:40,700 say we had a positive two Coulomb charge 62 00:02:40,700 --> 00:02:42,500 and we took that charge and we put it there 63 00:02:42,500 --> 00:02:44,400 at that empty point in space, 64 00:02:44,400 --> 00:02:47,033 before we put it there the V value was 100, 65 00:02:47,033 --> 00:02:49,100 when we stick it here, who cares? 66 00:02:49,100 --> 00:02:50,733 Why do we care about this 100 value? 67 00:02:50,733 --> 00:02:53,500 'Cause look at it, it's 100 Joules per Coulomb, 68 00:02:53,500 --> 00:02:56,600 that's what V, the Electric Potential, is telling us. 69 00:02:56,600 --> 00:02:58,966 So if it's 100 Joules per Coulomb 70 00:02:58,966 --> 00:03:01,533 and I stick two Coulombs there, 71 00:03:01,533 --> 00:03:03,600 how many Joules of energy do you think it's gonna have? 72 00:03:03,600 --> 00:03:04,866 It'll have 200. 73 00:03:04,866 --> 00:03:05,866 And that's the key, 74 00:03:05,866 --> 00:03:07,766 that's why we care about Electric Potential 75 00:03:07,766 --> 00:03:12,233 'cause it let's us find Electric Potential energy, 76 00:03:12,233 --> 00:03:13,700 either PE, sometimes people 77 00:03:13,700 --> 00:03:16,766 write Electric Potential energy as U. 78 00:03:16,766 --> 00:03:18,900 So the formula is just Q, 79 00:03:18,900 --> 00:03:21,446 you take the Q that you sticked at that point in space, 80 00:03:21,446 --> 00:03:23,800 in this case it was two Coulombs. 81 00:03:23,800 --> 00:03:25,500 Take whatever Q there is, 82 00:03:25,500 --> 00:03:30,467 multiply it by the value of the Electric Potential 83 00:03:30,467 --> 00:03:33,866 and that tells you how many Joules there would be 84 00:03:33,866 --> 00:03:35,800 for the charges in that region, 85 00:03:35,800 --> 00:03:37,633 so this Electric Potential energy is between 86 00:03:37,633 --> 00:03:39,400 these two charges here, 87 00:03:39,400 --> 00:03:41,300 the charge that created the V 88 00:03:41,300 --> 00:03:43,467 and the charge that you sticked at that point, 89 00:03:43,467 --> 00:03:45,200 and the V is a quick way to figure out 90 00:03:45,200 --> 00:03:48,500 how much Potential energy, Electric Potential energy 91 00:03:48,500 --> 00:03:49,566 there will be. 92 00:03:49,566 --> 00:03:50,900 So in other words, in this case, 93 00:03:50,900 --> 00:03:52,667 since I have two Coulombs there, 94 00:03:52,667 --> 00:03:54,133 I take my two Coulombs 95 00:03:54,133 --> 00:03:58,867 and I multiply by 100 Joules per Coulomb 96 00:03:58,867 --> 00:04:00,533 'cause that's the V value, 97 00:04:00,533 --> 00:04:04,800 and I get that there are 200 Joules 98 00:04:04,800 --> 00:04:07,900 of Potential energy now stored between these charges. 99 00:04:07,900 --> 00:04:10,800 So that's why we care about Electric Potential V, 100 00:04:10,800 --> 00:04:14,200 it's a way to figure out the Electric Potential energy 101 00:04:14,200 --> 00:04:17,266 for a charge that's placed at that point in space 102 00:04:17,266 --> 00:04:18,800 that has that V value. 103 00:04:18,800 --> 00:04:20,700 But, how do you get this V value? 104 00:04:20,700 --> 00:04:22,900 If I hadn't given you the 100 Joules per Coulomb 105 00:04:22,900 --> 00:04:24,333 we wouldn't have been able to figure this out, 106 00:04:24,333 --> 00:04:26,800 we need a way to figure out the V value 107 00:04:26,800 --> 00:04:30,567 at points in space based on the charges creating them, 108 00:04:30,567 --> 00:04:32,933 'cause charges create the V value. 109 00:04:32,933 --> 00:04:34,200 There's a formula for it, 110 00:04:34,200 --> 00:04:37,833 and the formula says that the V, Electric Potential, 111 00:04:37,833 --> 00:04:40,500 created by point charges equals K, 112 00:04:40,500 --> 00:04:45,500 K is the Electric constant 9 times 10 to the ninth, 113 00:04:46,000 --> 00:04:47,100 and it has units of 114 00:04:47,100 --> 00:04:51,466 Newton meter squared per Coulomb squared, 115 00:04:51,466 --> 00:04:53,033 that's always K. 116 00:04:53,033 --> 00:04:55,866 You take that K and you multiply by 117 00:04:55,866 --> 00:04:58,600 the charge that's creating the V value, 118 00:04:58,600 --> 00:05:01,100 so in this case is this Q, 119 00:05:01,100 --> 00:05:03,633 this positive Q here, whatever Q it is 120 00:05:03,633 --> 00:05:06,666 creating the V value that you wanna find, 121 00:05:06,666 --> 00:05:07,633 and that's key, 122 00:05:07,633 --> 00:05:10,200 if you plug in five Coulombs here 123 00:05:10,200 --> 00:05:13,166 you're finding the V created by that five Coulombs, 124 00:05:13,166 --> 00:05:15,267 if you plug in negative three Coulombs 125 00:05:15,267 --> 00:05:18,766 you'll find the V created by the negative three Coulombs, 126 00:05:18,766 --> 00:05:19,800 sometimes there's problems 127 00:05:19,800 --> 00:05:23,050 with multiple charges in it, like this one, 128 00:05:23,050 --> 00:05:27,073 and this Q gotta be the charge creating this V, 129 00:05:27,073 --> 00:05:30,566 not the charge you placed at that point in space, 130 00:05:30,566 --> 00:05:32,433 and I'll put the two Coulombs up here, 131 00:05:32,433 --> 00:05:35,633 but the charge creating the V value that I wanna find. 132 00:05:35,633 --> 00:05:38,233 And then you divide by the distance, 133 00:05:38,233 --> 00:05:41,800 so I divide by the distance between 134 00:05:41,800 --> 00:05:44,266 this charge and the point in space 135 00:05:44,266 --> 00:05:46,333 that I wanna figure out the V value at. 136 00:05:46,333 --> 00:05:48,033 Some people call this the radius, 137 00:05:48,033 --> 00:05:49,333 I don't like calling it radius, 138 00:05:49,333 --> 00:05:51,333 makes this sound like there has to be a circle, 139 00:05:51,333 --> 00:05:52,600 it doesn't really have to be a circle, 140 00:05:52,600 --> 00:05:54,967 this r would be the distance 141 00:05:54,967 --> 00:05:58,233 from this point of charge creating this V value 142 00:05:58,233 --> 00:06:01,000 to the point in space where I wanna determine the V value, 143 00:06:01,000 --> 00:06:03,066 that's r. 144 00:06:03,066 --> 00:06:04,900 So this is r. 145 00:06:04,900 --> 00:06:06,100 So how do we determine this? 146 00:06:06,100 --> 00:06:07,167 Let me just give you some numbers, 147 00:06:07,167 --> 00:06:12,167 let's say the charge we stuck here was one nanoCoulomb, 148 00:06:12,533 --> 00:06:15,366 nano is 10 to the negative ninth, 149 00:06:15,366 --> 00:06:18,266 so let's say that was one nanoCoulomb. 150 00:06:18,266 --> 00:06:20,667 And let's say the distance from this charge 151 00:06:20,667 --> 00:06:23,600 to this point in space was, 152 00:06:23,600 --> 00:06:26,866 let's say it was nine centimeters. 153 00:06:26,866 --> 00:06:28,866 And I wanna know what's the V value, 154 00:06:28,866 --> 00:06:29,900 well I can solve for it now, 155 00:06:29,900 --> 00:06:32,766 we got our formula, the V would equal, 156 00:06:32,766 --> 00:06:37,766 alright my K is 9, always, times 10 to the ninth, 157 00:06:38,467 --> 00:06:43,000 and it's Newtons meter squared per Coulomb squared, 158 00:06:43,000 --> 00:06:44,600 and then I multiply by my charge, 159 00:06:44,600 --> 00:06:47,000 and I told you that the charge here was 160 00:06:47,000 --> 00:06:52,000 10 to the negative ninth Coulombs, 161 00:06:52,148 --> 00:06:56,466 and my distance, I divide by the r value 162 00:06:56,466 --> 00:06:59,133 and the r value is nine centimeters, 163 00:06:59,133 --> 00:07:02,200 but be careful, everything's gotta be in terms of meters, 164 00:07:02,200 --> 00:07:03,966 kilograms and seconds 165 00:07:03,966 --> 00:07:06,066 when you're doing physics with constants. 166 00:07:06,066 --> 00:07:08,066 Look at this is in terms of meters, 167 00:07:08,066 --> 00:07:09,666 so I've got to use meters here, 168 00:07:09,666 --> 00:07:14,166 so nine centimeters is .09 meters. 169 00:07:14,166 --> 00:07:16,033 And if I multiply all this out 170 00:07:16,033 --> 00:07:17,900 what you'll get is, 10 to the negative ninth 171 00:07:17,900 --> 00:07:20,000 cancels this 10 to the ninth, 172 00:07:20,000 --> 00:07:24,000 the powers are 10, these just go away, 173 00:07:24,000 --> 00:07:27,800 and then I have nine divided by .09, 174 00:07:27,800 --> 00:07:29,966 that gets equal 100. 175 00:07:29,966 --> 00:07:31,333 So I chose this so that 176 00:07:31,333 --> 00:07:34,533 we got the same answer down there. 177 00:07:34,533 --> 00:07:36,100 Okay, 100 Joules per Coulomb, 178 00:07:36,100 --> 00:07:38,900 you might be like, where the Joules comes from? 179 00:07:38,900 --> 00:07:40,333 And how is this Joules per Coulomb? 180 00:07:40,333 --> 00:07:41,366 Well let's look at it, 181 00:07:41,366 --> 00:07:43,300 if we took, look at, 182 00:07:43,300 --> 00:07:46,700 one of these meters cancels one of these meters, 183 00:07:46,700 --> 00:07:49,300 and one of these Coulombs cancels one of those Coulombs, 184 00:07:49,300 --> 00:07:50,500 what are we left with? 185 00:07:50,500 --> 00:07:53,800 We're left with Newton times meter over Coulomb, 186 00:07:53,800 --> 00:07:56,833 but Newton times meter, that's force times distance, 187 00:07:56,833 --> 00:07:59,966 that's Joules, that's where we get Joules per Coulomb. 188 00:07:59,966 --> 00:08:02,600 So this really does give us the number of Joules 189 00:08:02,600 --> 00:08:04,700 there would be at a point in space 190 00:08:04,700 --> 00:08:07,566 per Coulomb of charge that you put there. 191 00:08:07,566 --> 00:08:09,000 And it works for any point, 192 00:08:09,000 --> 00:08:09,866 you pick any point, 193 00:08:09,866 --> 00:08:12,033 if I picked a point twice as close, 194 00:08:12,033 --> 00:08:15,400 it's half as far away, let's say some point over here, 195 00:08:15,400 --> 00:08:20,400 let's say this r value here was only 4.5 centimeters, 196 00:08:21,800 --> 00:08:23,566 well I'm dividing this by r, 197 00:08:23,566 --> 00:08:27,233 so if the r is half as big this point over here 198 00:08:27,233 --> 00:08:32,233 will have a V value of 200 Joules per Coulomb 199 00:08:33,100 --> 00:08:36,900 and the closer I get, if I went even closer, 200 00:08:36,900 --> 00:08:41,566 if I went to a point that was three centimeters away, 201 00:08:42,500 --> 00:08:45,866 well this is a third as much as this other distance, 202 00:08:45,866 --> 00:08:48,200 so if I'm only dividing by a third as much distance 203 00:08:48,200 --> 00:08:50,166 as you get three times the result 204 00:08:50,166 --> 00:08:52,633 'cause r is not squared, it's just r. 205 00:08:52,633 --> 00:08:53,800 So at this point, 206 00:08:53,800 --> 00:08:58,033 we'll have a V value of 300 Joules per Coulomb. 207 00:08:58,033 --> 00:08:59,933 This tells me, if I wanted to get 208 00:08:59,933 --> 00:09:04,800 a charge that have a whole bunch of Potential energy, 209 00:09:04,800 --> 00:09:06,600 I should put that thing nearby, 210 00:09:06,600 --> 00:09:07,866 I should stick it over here, 211 00:09:07,866 --> 00:09:10,366 this will give me a lot of Potential energy. 212 00:09:10,366 --> 00:09:13,066 Not quite as much, even less, 213 00:09:13,066 --> 00:09:14,866 the further I put my charge 214 00:09:14,866 --> 00:09:16,833 the less Potential energy it will have. 215 00:09:16,833 --> 00:09:20,700 There will be no Potential energy until there is a charge, 216 00:09:20,700 --> 00:09:22,300 there'll just be Electric Potential. 217 00:09:22,300 --> 00:09:25,833 But once you place another charge in that region 218 00:09:25,833 --> 00:09:27,600 to go with the first one, 219 00:09:27,600 --> 00:09:29,700 then you'll have Electric Potential energy 220 00:09:29,700 --> 00:09:32,566 and this will be a way to find it, 221 00:09:32,566 --> 00:09:36,400 Q times the V that you get out of this calculation. 222 00:09:36,400 --> 00:09:37,600 You gotta be careful though, 223 00:09:37,600 --> 00:09:39,666 sometimes people get sloppy, 224 00:09:39,666 --> 00:09:41,933 and V looks, you know, 225 00:09:41,933 --> 00:09:43,833 we use V for Electric Potential 226 00:09:43,833 --> 00:09:47,400 and we use V for Voltage, 227 00:09:47,400 --> 00:09:48,200 what's the difference? 228 00:09:48,200 --> 00:09:49,400 Are they the same? 229 00:09:49,400 --> 00:09:51,367 Hmmm, not quite. 230 00:09:51,367 --> 00:09:53,000 Sometimes you can treat them as the same 231 00:09:53,000 --> 00:09:53,833 and you don't get into trouble, 232 00:09:53,833 --> 00:09:56,066 but sometimes you do and messes you up. 233 00:09:56,066 --> 00:09:59,033 Voltage is a, technically a change 234 00:09:59,033 --> 00:10:01,667 in Electric Potential between two points, 235 00:10:01,667 --> 00:10:04,933 this is the difference in Electric Potential 236 00:10:04,933 --> 00:10:07,000 between two points in space, 237 00:10:07,000 --> 00:10:09,066 so it's got the same units 238 00:10:09,066 --> 00:10:10,866 'cause the change in Electric Potential 239 00:10:10,866 --> 00:10:13,400 still gonna have units of Joule per Coulomb, 240 00:10:13,400 --> 00:10:15,566 it's just, when it's a change in 241 00:10:15,566 --> 00:10:17,700 we give this a new title, 242 00:10:17,700 --> 00:10:20,933 we call the Joule per Coulomb unit a Volt. 243 00:10:20,933 --> 00:10:22,900 So Joules per Coulomb are Volts, 244 00:10:22,900 --> 00:10:26,233 but the word Voltage specifically refers 245 00:10:26,233 --> 00:10:28,766 to a difference in Electric Potential, 246 00:10:28,766 --> 00:10:30,166 what am I talking about? 247 00:10:30,166 --> 00:10:33,433 Well, look at, this point is 300 Joules per Coulomb, 248 00:10:33,433 --> 00:10:37,400 this point over here 100 Joules per Coulomb, 249 00:10:37,400 --> 00:10:39,166 so the delta V, if I were to take 250 00:10:39,166 --> 00:10:42,433 delta V between these two points right here 251 00:10:42,433 --> 00:10:45,267 and I ask, what's the difference in V? 252 00:10:45,267 --> 00:10:48,112 Well the difference in V is 200, 253 00:10:48,112 --> 00:10:50,800 200 Joules per Coulomb, 254 00:10:50,800 --> 00:10:53,433 that means the Voltage 255 00:10:53,433 --> 00:10:58,433 between those two points in space is 200 Volts, 256 00:10:58,767 --> 00:10:59,900 that's what it means. 257 00:10:59,900 --> 00:11:02,300 So, when you're talking about a difference 258 00:11:02,300 --> 00:11:04,500 in Electric Potential between two points in space 259 00:11:04,500 --> 00:11:06,233 we call it a Voltage, 260 00:11:06,233 --> 00:11:06,967 when you're talking about 261 00:11:06,967 --> 00:11:11,233 just the Electric Potential value at one point in space 262 00:11:11,233 --> 00:11:13,466 we call it the Electric Potential, 263 00:11:13,466 --> 00:00:00,000 and that's how they're related.