![]() ![]() You could think of them as male and female. Now they start moving towards each other! While electrons repel each other, and protons repel each other, an electron-proton pair seem to attract each other. We set up a new experiment, placing an electron and a proton one meter apart. The same law covers the interaction of electrons among themselves and protons among themselves. We know the mass of an electron to be 9.1 * 10^-31 kilograms, and we can substitute this in to get: F = (2.3 * 10^-28) / (dist^2)įor the protons we get the same equation. One newton is “the force required to accelerate one kilogram by 1 m/s every second”. ![]() We measure mass in kilograms, and force in “newtons”. We can substitute F=ma into our equation to get: F = (K*mass)/(dist^2) ![]() We saw that increasing the mass (from an electron’s to a proton’s) resulted in decreased acceleration, and decided from this that the force was constant. For a fixed force, increasing the mass results in decreased acceleration. Force is mass times acceleration ( F=ma). We decide that in both cases - for electrons and protons - the particles must be imparting a “force” on each other. Because protons are much more massive than electrons, they accelerate much more slowly. The sluggishness is simply proportional to the amount of mass. A proton has the mass of about 1800 electrons. It turns out we know the mass of electrons and protons. For protons, K is 0.14 around 1800 times slower. ![]() We find the same behavior, but much more sluggish: at one meter apart, the protons accelerate away from each other at about 14 cm/s^2. Now we do the same experiments, but with protons. We’ve already done so, and found the acceleration to be 253 m/s^2. What is K? This can be found experimentally: set the distance to one meter, and measure the acceleration. Now we can try to find an exact equation with a coefficient: acc = K/(dist^2) The units don’t matter here, but let’s get specific: the acceleration is in m/s^2, and the distance d is in meters. Here, acc is the acceleration of the electron, and dist is the distance from the other electron. We draw up this proportion: acc ∝ 1/(dist^2) It seems the force follows an inverse square law. At four meters apart, half again: around 63 m/s^2. Placing the electrons two meters apart, they experience only half the acceleration around 126 m/s^2. When set further apart, the acceleration is less strong. When we set the electrons one meter apart, A flies from B with acceleration of about 253 m/s^2. It seems the force depends on the distance. We then find that they start to move away from each other! What’s going on here?īy observation, we see that they move away from each other very quickly when they are close, but less quickly when they are far away. We have two electrons, A and B, and we put them in space, with nothing else around. To see, let’s set up an imaginary experiment. Equivalently, the current across a boundary is the number of electrons crossing one way, minus the number of protons crossing in the same direction.īut why do we talk of charges cancelling out? Why do we talk of net flow? What is it that causes this “current”? When we talk of “current” over a boundary, we mean the net flow of these charges across this boundary. When we talk of the “charge” of an aggregate object, we’re measuring the sum of these charges. Electrons carry 1e of charge, and protons carry -1e of charge. Electric charge is a thing carried by fundamental particles: electrons and protons. In previous posts I described electric charge and electric current. ![]()
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