ï»¿ Electric fields just like forces are vectors, we have to add them according to our vector rules. So let's say we have the following, let's say we have a positive charge sitting right there, we have a positive charge sitting right there, and we're gonna look for the electric field at this location right here. How do I figure out e at this location? Well they're vectors, so the electric field from this one is going to come out radially, which means up here it's going to be pointed in that direction. The electric field from the other one is also radial from its center, and so it will be pointing down in that direction. And now if I add two vectors like that, I know what they have to be. It has to be all to the right, they're gonna cancel out vertically, they're gonna contribute horizontally, and you get a net electric field that is in that direction. So just looking at this picture you can identify a few things right off the bat. For instance if I am right here, halfway in between those two charges, what's the electric field? What's the net electric field right there? Sam you said it, zero, right? It's got to be zero because the top one is pushing down, the bottom one is pushing up, those electric fields perfectly cancel and you get a neck--a net electric field of zero. If I'm over here, I have the exact same problem as this just on the other side, and so I'm going to get something going to the left. Okay, so that is adding these electric fields you have to be careful and make sure that you regard them as vectors. Okay, so what is the strength of these electric fields? Well the strength is the following, what we said was e is f over Q naught. The magnitude is just going to be the magnitude of F divided by Q naught, and here F is Coulomb's law. So it is K times Q times Q naught divided by R squared, and all of that is going to be divided by Q naught, and so the Q naughts cancel out and we get K Q over R squared. This is the magnitude of the electric field and if you want to write it back as a vector, you can say this, KQ over R squared R hat. Okay, and R hat is the direction and its radial from the charge Q. So here's my charge Q, capital Q. Okay, let's say it's positive and let's calculate the strength of the electric field here. Well we know what the electric field looks like, it's pointing radially outward, it drops off like 1 over R squared, so these arrows get a little bit shorter as you go out and you can draw as many as you like. Now let's say I want to calculate the electric field a distance R away from the center. I drew a point here where there's no arrows, does that mean there's no electric field there? No, of course not, the electric field is everywhere out here, we just don't want to draw an infinite number of arrows. So the electric field at this point still exists and that electric field is going to be K times the charge, which we said was capital Q divided by R squared and the direction is R hat radially outward. So we draw with an arrow right there. Gets weaker as you go out because it falls off like 1 over R squared, the direction is always away from the point charge and it has a strength that increases with the amount of charge capital Q.