# Electromagnetic black hole?

So I was thinking about something for the past while

Consider a large spherical foam-ball with homogeneous density. Where a foam ball is defined as an object that can absorb matter with 0 friction (example: a gravitational well without an object inside). This is a purely theoretical construct.

If the foam-ball has a radius R and a charge Q. What charge must the foam-ball have, such that there is well defined sphere or horizon such that any object with a negative charge (even if it is the slightest bit) must travel faster than C in order to escape the field of the ball.

Aka what charge would turn this into a black-hole for all objects with opposite sign on their charge?

Once again I assume the foam-ball is a single particle, that doesn't repel itself... its just a very large homogenous 'thing' with charge.

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Can this approached using a similar style of math as the construction of a gravitational black hole, except mass is substituted with charge, etc... ? – frogeyedpeas May 28 '13 at 19:14
I think you should just use basic equations as $F_e = k*\frac{Q_1*Q_2}{r^2}$ and $a = \frac{F}{m}$. You then put e constant instead of $Q_2$. I'm only not sure how to deal with aceleration. – Tomáš Zato May 28 '13 at 19:24

However, if you fix the negative charge at some value $q_2$, it will be unable to escape when its electromagnetic potential energy equals its rest energy (up to a sign). So just set $\frac{1}{4\pi\epsilon_0}\frac{q_1q_2}{r} = mc^2$ (again, up to the correct sign) and solve for $r$.
Yep, try here. It explains how to derive relativistic escape velocity in a gravitational field, and you should see $m_0$ divide out in the algebra. – Izzhov May 28 '13 at 19:46