Concenctric spheres and electron

[masacre]

Homework Statement

Inside evenly charged (with charge Q < 0) sphere with radius R is evenly charged sphere with potential equal to potential in infinity and radius R/2. Both sphere are concentric.
From internal sphere, tangentially to it fly out electron (with charge e < 0). What is minimal initial kinetic energy of the electron E so it can reach external sphere? Electron speed is much smaller than speed of light.

Homework Equations

The Attempt at a Solution

External sphere does not have effect on electron because electric field inside a sphere is zero (Gauss's law), am I right? Potential in infinity is equal to zero so in inital moment charge on internal sphere is equal to zero. After the electron fly out of it its going to have charge equal to e (e > 0) and therefore it has effect on electron. My question is whether or not this new charge induces additional charges on external sphere and those additional charges have effect on electron?

 

[collinsmark]

Hello masacre,

Homework Statement

Inside evenly charged (with charge Q < 0) sphere with radius R is evenly charged sphere with potential equal to potential in infinity and radius R/2. Both sphere are concentric.
From internal sphere, tangentially to it fly out electron (with charge e < 0). What is minimal initial kinetic energy of the electron E so it can reach external sphere? Electron speed is much smaller than speed of light.

Homework Equations

The Attempt at a Solution

External sphere does not have effect on electron because electric field inside a sphere is zero (Gauss's law), am I right?

Yes, and no.

You are correct that the external, spherical shell does not affect the motion of the electron (all else being the same). The evenly distributed charge on the external, spherical shell does not affect the electric field within the shell; thus it doesn't have a direct effect on the electron.

But you are not correct that the electric field within the external, spherical shell is zero (i.e. between R > r > R/2). That's because there is the internal sphere inside.

Gauss' law states that the electric field inside a evenly distributed, charged, spherical shell is zero, only if there are no other charges around. But in this case, the inner sphere does have a charge on it.

Potential in infinity is equal to zero so in inital moment charge on internal sphere is equal to zero.

That's not correct either. Just because the electric potential at surface of the internal sphere is equal to zero (with respect to infinity), does not mean that the charge on the internal sphere is zero.

If it helps, consider a different situation. Suppose that there is no internal sphere at all, but there is still the external, spherical shell with some evenly distributed charge on it. In this other, hypothetical situation, because there is no electric field inside the shell, it means the electric potential inside the shell is constant (i.e. uniform). But that does not mean it is zero. It just means that the electric potential is constant at all points within the shell.

This problem is different than that though. In this problem the internal sphere must have some charge on it in order to bring the potential back to zero at the surface of the inner sphere (otherwise the potential inside the external shell would be a non-zero constant).

After the electron fly out of it its going to have charge equal to e (e > 0) and therefore it has effect on electron.

I'm guessing that for this exercise, you can neglect the small change in the charge of the internal sphere as an electron flies out.

My question is whether or not this new charge induces additional charges on external sphere and those additional charges have effect on electron?

I'm guessing that you are supposed to neglect induced charges (or anything similar to that) for this problem.