Electric Field Lines

Hey guys. Let's do another example of drawing electric field lines, okay? Draw the electric field lines for the four Chargers shown below this arrangement is known as an electric quadripole, okay? So, just like we had an electric dipole which was two charges, di 2, we have an electric quadripole, Quadra being four, charges arranged like shown, okay? The important thing to remember here is that the electric field decreases pretty rapidly with distance, okay? The electric field is what we call directly proportional to 1 over r squared that means that, when r doubles that two is actually squared. So, E becomes one over four, when r triples he becomes one over nine. So, it's not just that it drops off linearly it drops off very, very rapidly like this, this is the electric field versus r, basically what I'm getting at is that only nearby charges affect the electric field lines. So, we can do is we can actually look at this as a collection of multiple dipoles and our electric field lines are going to look like that, okay? So, let's start.

These dipole lines are going to go from the negative, sorry, from the positive to the negative, is the other direction, okay? These dipole lines are going to go from the positive to the negative, these dipole lines are going to go from the positive to the negative and these dipole lines are going to go from the positive to the negative with very, very little influence. Now, the closer we get to the center the more it looks like a dipole, sorry, the less it looks like a dipole the more we get away from the center the more it looks like a dipole, so the further away this actually looks even more like a dipole the further away this looks even more like a dipole this one looks even more like a dipole, okay? Now, what happens as we get near the center? Well, at the very center we have an electric field down due to the top positive charge, we have an electric field up due to the bottom positive charge, we have an electric field to the left due to the right negative charge, sorry, 2 to the left negative charge and we have an electric field due to the right, to the right, due to the right negative charge, okay? Because all these charges are the same and because we're looking at the direct center so they're all the same distance from the center, we know that all of these electric fields cancel so the electric field is just going to be 0 at the center of the dipole, sorry, it's a quadrupole, okay? So, this is what it looks like, it looks like a collection of dipoles with a 0 electric field at the center.