**Concept:** Intro to Current

Hey guys. In this video we're going to start shifting gears from what we've been predominantly talking about in the past, okay? Previously, we've pretty much been focusing on charges at rest, which we would call electrostatics. Now, we're going to talk about charges in motion, which we would call electrodynamics, and we're going to start in this video with currents. Alright, let's get to it. What a current is it's just a flow of charges, okay? If a bunch of charges that are moving together, kind of like a liquid, that's what the current is, let's imagine we have a capacitor that has some positive charge on one plate and some negative charge on the other plate, if I string a conducting wire between the two, electrons on the negative plate are going to leave and move towards the positive plate because they're attracted to the positive plate, right? That's going to form a current in that wire of electrons moving to the left. Now, the thing is that by convention the current always points in the direction of the flow of positive charges, okay? So, if we look at these two plates, the positive on the left and the negative on the right, if positive charges were moving they'd be moving from the positive plates to the negative plates, so that is the direction of the current by convention. Now, current represent as an I, okay? Why does this convention exist? It's because when current was discovered, hundreds of years ago, it was way before the electron was discovered and they had a 50/50 shot of guessing whether currents were made of positive or negative charges, they guessed positive, they got it wrong, okay? Now, for some reason that conviction still existed. So, just keep it in mind, okay? Now, we've talked about this before, why do these charges move through conductors? Why would charges move through a conducting wire? The motivation is provided by voltage, okay? A potential difference, whenever a voltage is put across a wire those charges will move through that wire, alright? Now, there's another name for voltage, because there aren't enough names already, that you guys are probably going to come across, which is called EMF the electro-motive force, just know that an EMF is not a force, as it's called, it's just a voltage, it's just another name for voltage, it's really old, okay? But for some reason people still use it? Well, typically for voltage you're going to see V, you should see V for an EMF because it's the same thing but sometimes they use this fancy E instead, okay? So, if you see the word EMF, if you see this fancy E, just know that that's still voltage, okay? Nothing has changed. Now, mathematically, current is defined as the amount of charge passing through some point per unit time, right? The amount of charge divided by the amount of time, basically, if I were to draw an imaginary sort of hula hoop, right? A plane that charges in this conductor could move through and I started a stopwatch and I waited, let's say a second, and counted the amount of charge passing through, if I divided that by one second, that would be my current, okay? It's just the amount of charge moving through a point per unit time. Now, the units of current are amps, okay? Given by a capital A, and as you can see from our equation for current, that's just charged per time. So, one amp is 1 Coulomb per second, okay? No big deal, let's do a couple of examples to close this out, if the capacitor initially charged to 5 nanocoulombs has a wire connected between the positive and negative plates, what would be the current in the wire, if it takes 10 milliseconds to completely discharge, right? Current, we know is Delta Q, over delta t, in order to calculate that we need to know, how much charge is moving and how long it takes that charge to move, we are told that 5 nanocoulombs is going to move from one place the capacitor to the other and it's going to take 10 milliseconds. So, we have everything, we need to solve this problem, don't forget that a nano is 10 to the negative 9 and the milli is 10 to the negative 3. So, dividing those, we get 5 times 10 to the negative 7 and the units for current once again, are amps, super simple, no big deal.

Let's do the second example. 1 milliamp of current passes through a wire how many electrons pass through the wire in five seconds. So, once again our definition of current is Delta Q over delta t. Now, we do know the current and we do know the time. So, we could find Delta Q but that's not what we're asked for, what we're asked for is the number of electrons. So, we need to relate some charge to a number of electrons, we do have a really old equation that we used a while ago, that says, charge is a number of protons minus the number of electrons times the electric charge? Well, in this case protons aren't moving, all we're dealing with are electrons, so this is going to be negative number of electrons times the elementary charge, this is going to relate our charge, which we can find with this equation, to our number of electrons. Alright, good to go, let's solve this problem. Delta Q is going to be i delta t, all we have to do is multiply delta t up, which is going to be 1 milliamp, a milli is 10 to the negative 3, times 5 seconds so this is 5 times 10 to the negative 3 Coulombs, a little bit about this negative sign, okay. If we just proceed as is we're going to get a negative number of electrons, which makes no sense. Now, by convention the current never carries a sign, okay? We always have the magnitude of the current. So, this number right here, is the magnitude of the charge. Now, since this charge is carried by electrons it should be negative, okay? That's going to take care of the negative sign when we combine these two equations, let's do that now, we know that the charge transferred is going to be negative number of electrons times E, rearranging that, the number of electrons is negative Delta Q over E, okay? So, the number of electrons is just the negative of the negative 5 times 10 to negative 3, the charge of the electron is 1.6 times 10 to the negative 19, right? The elementary charge, which you guys should remember, this all works out to be 3.12 times 10 to the 16 electrons, okay? Once again, no big deal, just two pretty straightforward equations. This wraps up our introduction to current. Thanks for watching guys.

**Problem:** A lightning bolt hits the ground carrying a current of 3 x 10 ^{4} A. If the strike lasts 50 ms, how much charge enters the ground?