# Ratio of potentials and charges on two spheres

1. Homework Statement
Consider two "solid" conducting spheres with radii r1= 4 and r2= 1. I.E., r2/r1= 1/4.

The two spheres are separated by a large distance so that the field and the potential at the surface of sphere #1 only depends on the charge on #1 and the corresponding quantities on #2 only depend on the charge on #2.

Place an equal amount of charge on both spheres, q1=q2=Q.

After electrostatic equilibrium on each sphere has been established, what is the ratio of the two potentials V2/V1 at the "centers" of the two solid conducting spheres?

What is the ratio of the electric fields E2/E1 at the "surfaces" of the two spheres?

2. Homework Equations
As near as I can figure out:

q= charge
r= Displacement from the reference point in the direction of the field

Delta V= Kc (q/r)

E= Magnitude of the electric field
d= Displacement

Delta V= -E Delta d

3. The Attempt at a Solution

At first, I set the charge on each at 10 for the sake of convenience, than ran the numbers through the formula. I ended up with V1= 2.2475e10 and V2=8.99e10. When V2 was divided by V1, I ended up with a ratio of 4.

As far as electric fields went, I ran the second formula and then divided E2 by E1 for a ratio of 16.

Did I work this problem correctly?