![]() The answer can be found by just changing up some stuff. Or is it wrong because my step size is too big? Why is it wrong? Is it because I started at y = 0.5 meters (I just realized I’ve been using the variable y instead of x-but it should be fine). Notice that gives a close, but wrong answer (compared to my previous calculation). Now I can use this same calculation go find the work needed to move the electron. But still, this is good because it looks like the calculation is working. Note that I started from just 5 cm away from the origin-which is TOTALLY not infinity. Over this distance, assume the force is constant and calculate the small work done-add this to the total work.īefore making this one program, I’m going to just make a program to plot the electric field from some value up to point B.Move some short distance towards point B.Calculate the total electric field and the force needed to push the electron at this point.It just needs to be far enough away such that the electric force is negligible. Start at some position far away (but not actually infinity because that would be crazy).I wrote the force and displacement as scalars because it’s just the magnitude that matters. Also, the angle between F and the displacement is zero. This is the force needed to PUSH the electron (with a charge e)-it’s not the electric force on the electron (which is in the opposite direction). That means the tiny amount of work (which I will call ) would be equal to: If this distance is short ( ) then the force is approximately constant. Keep repeating this until I get to point B. ![]() During this tiny move, the electric field (and thus the force) will be approximately constant. Instead of calculating the total work to move the charge to point B, I’m just going to move it a tiny bit. We can’t use the above formula to calculate the work-unless we cheat. So, as you push a charge towards point B (point A is boring-for now) the electric field changes. ![]() Oh, and the force will be the opposite of the electric force where: Remember that work-energy principle? It says this:Īnd the work can be defined as the following (if the force and displacement are constant): Now I’m at positive infinity y-and I just did that problem. The electric field is zero out there, so that requires zero work. I’m going to move in a circle from positive infinity x to positive infinity y. Remember that for electric potential, the path doesn’t matter-only the change in position (path independent). You want to get to A from a point of infinity on the positive x-axis? OK. But that requires ZERO work since the force and displacement are perpendicular. You would have to push it in the positive x-direction and move in the y-direction. That means the electric force is in the negative x-direction. As you move down the axis to point A, the electric field is in the x-direction. How about this? Suppose you take the electron from infinity on the positive y-axis. Yes, the energy needed to put a point charge at A from infinity is zero Joules. When added together, the total potential is zero volts. Since they have the same distances but equal and opposite charges, the two potentials will be opposite. What about point A instead of B? Well, in this case, I just have different distances. Putting this all together, I get the following. The distance will be 6 mm and the distance will be 4 mm (need to convert these to meters). ![]() That means the total potential will be:įrom the original problem, and. Let me call the positive charge “1” and the negative charge “2”. Since there are two point charges, the total potential will just be the sum of the two potentials. Where k is the Coulomb constant ( and r is the distance from the point charge to the final location. Since I am dealing with two point charges, I can use the following expression for the potential due to a point charge (with respect to infinity): Yes, you could also calculate the work needed to move the charge-I’ll do that also. That means I just need to calculate the change in electric potential from infinity to point B. The energy needed would be equal to the change in electric potential energy which is equal to: Let’s start with the energy to bring an electron to point B. But let’s just start with a problem and then solve it in more ways than you wanted. This connection between the electric potential (change in electric potential) and the electric field can get sort of crazy.
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