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Electric Fields equation force

  1. Jan 22, 2008 #1
    Electric Fields is being taught in my A-level physics course but I don't really get it.

    Firstly, we are given the equation Force= (Q1*Q2)/4*pie*permittivity*r^2 . But I don't know how it is derived. What area of Electric Fields should I research into to begin with?
  2. jcsd
  3. Jan 22, 2008 #2


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    Imagine a single point radiating energy, or a field or whatever you wish. For instance, light, let's suppose a single point source of light is emitting light in all directions. We then assume energy is conserved, and that the point source emits exactly 1 "instant" of time. So we can trace the paths of each wave, and to keep things simple, just model it as an expanding sphere. So our original sphere of light at t=0 has a radius of 1 (just for the sake of simplicity). Doubling the radius of the sphere, to 2, will quarter the intensity of the light - (for an example, see this image which should hopefully do a far better job explaining).

    That determines the intensity for a general case - you can think of this as a coefficient to multiply something (in this case, we just took the value 1), which tells you how large something will be after you set the radius to whatever.

    You then introduce force, because, well, that's what you want to measure. At r=1, the force per surface area is also 1. But at r=2, the force per unit area is then 1/2^2 or 1/4 (see diagram). So now we have a general equation that shows how force per unit area (for example, light intensity, pressure, etc) changes as a function of distance from the point source and also with a certain initial force to be distributed. That's all fine and dandy in magic units, but we use the metric system. And that, is where 1/4*pi*e(0) comes in, to compensate, just like you have a gravitational constant (big G, not the acceleration/force), and just as you have the speed of light defined as 3*10^8 metres (actually, the metre is defined as 1/3*10^8 of the speed of light).

    So yes, inverse square laws and compensation factors, nothing more. To get the force law, just multiply by the charge of the second item. A net positive force results in repulsion, a net negative force results in attraction. In any case, it's all formalism and models, it doesn't mean that what you're looking at truly follows your ludicrously simplified description (especially in this case). As for research, you want to hit Google for things like Coulomb's law and inverse square laws.
  4. Jan 22, 2008 #3


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    Staff: Mentor

    The electric force law basically comes from experimental measurements, starting with Charles Coulomb in the late 1700s. The [itex]1 / 4 \pi \epsilon_0[/itex] factor is a proportionality constant, chosen so the numbers come out correctly for the given units of charge, force and distance. It has that funky form rather than a simple k or something, to make other equations come out simpler-looking later.
  5. Jan 22, 2008 #4
    It was established experimentally and I believe can be derived from Maxwell's equations
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