Thread: Electrostatic Force Problem

Actually there is kind of a way which bypasses my lack of knowledge about solving the above (which I'm learning about at the moment actually), as you can prove with vector calculus that the electrostatic potential energy of two particles is q1*q2/(4*pi*epsilon0*r).

The particles will have maximum velocity when all of this has been converted to KE (at a separation of infinity), so equate the sum of their final kinetic energies to the above quantity, and then you can use the conservation of momentum (which sums to 0 here), sub that in to eliminate the other velocity, and hence get the final velocity of one of the particles.

My final result is v1 = sqrt(q1*q2*m2 / (2*pi*epsilon0*r*m1*(m1+m2))).

And obviously the symmetrical result for v2.

But as the seperation distance approaches infinity that equation will go to zero, no?

No, r is the initial separation which is all that matters because you're calculating the energy of the whole system which is constant.

I plugged in the numbers but the velocities that come out of it are too small I think. I got 13.9 m/s for the lighter sphere and 4.25 m/s for the heavier sphere.

However, the accelerations were 261 m/s^2 and 80.1 m/s^2.

Why do you think those values are incorrect?

Given those large accelerations, the particles only need to accelerate for a fraction of a second before the electrostatic force has decreased by a large factor and their accelerations become neglibible.

I could of course have slipped up in deriving my formula (I get the same numerical answers as you). Try it yourself and check that it comes out okay.

Hey Xei what you said makes sense I didn't really think of that :/

It turns out those values are correct, thanks a lot for the help!

Any time. I needed something to warm up with today anyway.