It's evenly distributed throughout, then this formula also works just as well when you're If you're outside of this charge and you've got a spherically symmetrical charge distribution, where all the charges are lumped on one side of this sphere, or anything like that, if Or, if this is spherically symmetric, then it doesn't matter. Really, really small compared to the otherĭimensions in the problem. Technically, though, this is only true if this is a point charge. This is a formula for the electric field created by a charge Q1. The field to the point in space where you wannaĭetermine the electric field. We can just figure out the electric field that's created by Q1Īt any point in space, so this r is just theĭistance from the center of the charge creating But since this Q2 always divides out, we don't even need to talk about that. Wherever I wanna figure out what the electric field would be. The r would just be the distance from the first charge, Q1, to I could put it here, IĬan move it over to here. So you imagine your testĬharge at any point you want. Centered between which two charges? Well, this could be to any Those two charges squared, and you might be like, well, And then, what do we still have up here? We've still got a Q1 divided by the center to center distance between K is nine times 10 to the ninth, and it's got kinda weird units, but it makes sure that all the units come out okay when you multiply. Get that the magnitude of the electric field is gonna be equal to k, this electricĬonstant, and I'll write that down over here so we know what it is. Then because we're finding electric field in here, Other charge interacting, divided by the center to center distance between them squared, and That'd be this Q1 over here, multiplied by Q2, the Times 10 to the ninth, multiplied by Q1, the first charge that's interacting, and Coulomb's Law says that the electric force between two charges is gonnaīe k, the electric constant, which is always nine Coulomb's Law gives us theįorce between two charges, and we're just gonna Is simply by inserting what we already know is theįormula for the electric force. The way we'll find aįormula for the magnitude of the electric field This formula we get will just be for the magnitude of the electric field, and I'll tell you why in a second. So I'm gonna erase these vectorĬrowns on these variables. We're about to find here is gonna be for the magnitude Is there a formula for that? There is, and it's not that hard to find, but the first thing I'll caution you about is that the formula Over here at this point in space, without even What's the electric field that this Q1 is creating It'd be useful to have a formula that would let us figure out What's the electric field being created at that point in space, without even referring to Q2. If we took the force on this charge Q2 divided by Q2, that wouldīe the electric field at that point in space,īut something that would be useful to have is a formula that would let us figure out Let's call this Q2, so we can keep these all straight, and I'll call it Q2 up here. If we took the force on this charge, and let's give this a name. Its way into this region, let's say this charge right here. Of the electric field is the amount of force per charge. For more information on this topic, an excellent starting point is the video “ Quantum Invariance & The Origin of The Standard Model” referenced at the end of this section.- Okay, so we know that electric charges create electric fields. (In fact, the electromagnetic force is found to be one of just four fundamental forces, the others being gravity, the strong nuclear force, and the weak nuclear force.) Quantum mechanics also facilitates greater insight into the nature of electric charge and of the photon, which is the fundamental constituent of electromagnetic waves. However, a deeper understanding is possible using quantum mechanics, where we find that the electric field and the magnetic field are in fact manifestations of the same fundamental force, aptly named the electromagnetic force. This is the best we can do using classical physics, and fortunately, this is completely adequate for the most engineering applications. We have have not directly addressed the question of what the electric field is. The reader may have noticed that we have defined the electric field in terms of what it does. \( \newcommand\) is the rate of change in electric potential with distance in this direction.
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