What if... you had a bowl of electrons? My chemistry teacher used to tell us that if you had a soup bowl with only electrons in it, the explosion could make you fly to Pluto. Was he right? Could this happen?
 A: A uniform sphere of radius $r$ and total charge $Q$ has an electric potential energy of $3Q^2/20\pi \epsilon_0 r$.
Let's say your bowl is like a sphere of radius 5 cm. If it's all water ( molecular weight 18$m_u$) and $\mu= 9/5$ of a mass unit for every electron, then the number of electrons is
$ N_e = 1000 \frac{4\pi r^3}{3}/\mu m_u = 5\times 10^{26}$
If all the nuclei were removed, the electric potential energy would be $7\times 10^{26}$ Joules.
Pluto is at about 40 au from the Sun, effectively to get there, you have to escape from Earth and escape from the Sun. To do this you would need to launch from the Earth with a carefully directed speed of at least 16 km/s. If your mass is 100 kg, that takes a mere $1.3\times 10^{10}$ J.
A: The answer would depend how densely the electrons are packed. Let's say we have 1 kg of electrons, meaning we would have about $N = 10^{30}$ of them. For simplicity, let's approximate by arranging all of these electrons arranged in a spherical shell of radius $r=0.1$ meters. By symmetry, the voltage at the location of each charge would be constant and would have the following value.
$$V = -\frac{1}{4\pi \epsilon_0}\frac{Ne}{r}$$
We can thus compute the potential energy $U = \frac{1}{2}Q V$ associated with this configuration.
$$U = \frac{1}{2} \cdot Ne \cdot \frac{1}{4\pi \epsilon_0}\frac{Ne}{r} = \frac{N^2 e^2}{8 \pi \epsilon_0 r} \approx \boxed{1.15 \times 10^{33} \text{ Joules}}$$
Ignoring air friction, the Earth's escape velocity is $v =11200$ meters / second, which for a $m=2\times 10^6$ kg space shuttle, would only require $E = \frac{1}{2} mv^2 = 1.25 \times 10^{14}$ Joules.
So, yeah, you'd have way more than plenty sufficient energy.
