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Anderson Video - Electric Field Lines

Professor Anderson
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 Hello class. Welcome back to another learning glass lecture on physics. We're talking about electric fields today and we touched a little bit on this last time but let's review just a little bit. What's an electric field? So an electric field we write with a capital E. Okay, and the electric field is defined as the force that a test particle would see divided by the charge of that test particle. What does that mean? Well, let's say we have a big positive charge right here. Okay, that positive charge is going to exert an influence on a test charge. If this happens to be a positive charge then we know what's going to happen, right? We talked about what happens to charges of the same sign, we said that likes repel. And so there is a force here, F, which is pushing that particle away, right? Those two positive charges are going to separate. Okay, but let's say we don't have any charge there. Let's say we just erase it and we think about that region of space. And let's say that we are a distance R away from our charge and that charge has a total value of Q. What can we say about the electric field in this region? And what do we even mean by electric field? What we mean is if I put a test particle there, would it experience a force? And if the answer is yes, then there is an electric field there, if the answer is no, then there's zero electric field there. All right, in this case we know that it will experience a force, so there must be an electric field there and the electric field is apparently F over Q naught. But we know what F is, F is Coulomb's law. So that becomes K Q Q naught divided by R squared, we're gonna divide that whole thing by Q naught and there is a particular direction associated with this. Okay, we typically call that R hat. What is R hat mean? That's out radially, so if you have a point charge sitting at the origin, this is our XY coordinate system. Remember we talked about polar coordinates, R is along a radius so R hat is a radial unit vector, it's pointing away from the origin in this case, it would be pointing away from the charge. Okay, we can cross out the Q naughts right away and so this whole thing simplifies to the following: K Q over R squared R hat, and this is the electric field of a point charge and this is a good thing to just burn into your memory. Electric field of a point charge: E is KQ over R squared, R hat. That R hat is just the direction, it means pointing away from the point charge. All right, so let's draw some electric fields. And just make sure we're all on the same page, if I have a positive charge, electric field lines go out from that positive charge and if I draw it with continuous lines, like so, the arrows indicate the direction of the electric field. The lines indicate those lines of electric field, the density of those lines indicates the strength. Where the lines are tight together, the electric field is strong. Where they are spread out electric field is weak. Positive charges we call sources, electric field lines come out from positive charges. Negative charges are called sinks, the lines look exactly the same but what changes is the direction of the arrow. It's now pointing towards the negative charge and those field lines end on the negative charge. Those we call sinks. So think about these words, sources and sinks, right. The source is like your faucet in your bathroom, you turn on the faucet water comes out. The sink is where it drains into, it's where it disappears from your bathroom. Sources and sinks, positive and negative charges All right. That's not too bad. When we put them together, we get the dipole field and we talked about this a little bit earlier and the dipole field looks like this, it goes out of the plus, into the minus and you can draw as many as you like. Okay, this is a dipole field. Lots of things in the universe are of course dipoles, and so this becomes an important field to be concerned about, the dipole field.