# Escape velocity of E-field

1. Oct 28, 2013

### kickthatbike

Upon applying the method of finding escape velocity to the E-field, I end up with:

$\sqrt{\frac{2kQq}{rm}}$

What I don't understand, conceptually, is why escape velocity decreases as mass increases, in the electric field. What property is actually taking place here?

2. Oct 28, 2013

### Staff: Mentor

More kinetic energy is invested in a mass for a given velocity if the mass is larger. When dealing with the gravitational field, the force providing the potential energy scaled with the mass, but the inertia and thus the KE of the moving mass also scaled with the mass. This is due to what's known as "the equivalence principle", wherein gravitational mass and inertial mass are numerically the same for all matter. The effects cancel in the equations and the mass of the "escaping" body drops out of the equation for escape velocity.

With the electric scenario there's no equivalence principle "hiding" the effect of the mass of the moving object in the relationship. The electric force does not depend upon the mass of the object in motion, but the inertia and thus KE still depend upon that mass. So, for a given v: small mass, small inertia and small KE. Large mass yields large inertia and KE. The electric potential energy change, which the KE must balance for asymptotic escape, remains fixed by the charges.

3. Oct 28, 2013

### kickthatbike

You explained that very well. Thank you very much.