Electrostatics - metal sphere potential

[xwhyy]

Hi,

again very simple problem

Homework Statement

Metal sphere of radius R1 is charged to 10V.
It is then connected to another sphere with R2 = 2*R1.
What is the final potential?

Homework Equations

The Attempt at a Solution

V = E * distance
so in the case of disconnected it is E*R1
when connected R's sum up so it would be E*(R1+R2)
and since I don't know E but R2=2*R1
it is E*3*R1 so my solution is:

V_connected = V * 3

Is that correct?

 

[SammyS]

If it's correct, that's only a coincidence.

What is the potential of a sphere of radius R₁ and charge Q?

Set that equal to 10V and solve for Q.

Then distribute the charge over the two spheres so that their potentials are equal.

 

[xwhyy]

Thank you for your reply!

so:

V = Q / [4*pi*epsilon*r1]
Q = V * 4* pi * epsilon * r1

V_connected = (V * 4 * pi * epsilon * r1) / ( 4 *pi * epsilon * 2 * r1)
which after simplification is equal
V_connected = V/2

is that true? :)

 

[xwhyy]

hop hop

 

[SammyS]

...

V = Q / [4*pi*epsilon*r1]
Q = V * 4* pi * epsilon * r1

Looks good. BTW: V = 10 Volts

When they're connected: V₁ = V₂ and Q₁ + Q₂ = Q = V·4πε₀·R₁.