Work required to separate parallel plate capacitors

[avolp]

Homework Statement

A parallel plate capacitor with capacitance C is charged to a value q and then isolated. The separation between the plates is then tripled. What was the work required to separate the capacitors?

Homework Equations

U=1/2CV^2
Q=CV
C=ε0A/d

The Attempt at a Solution

W=ΔU=1/2C₁V₁^2-1/2C₂V₂^2
=1/2C*(Q/C)^2-1/2*(C/3)*(Q/C)^2
=Q^2/3C
I tried this but this wasn't the correct answer and I can't figure out why. Thank you in advance for the help

 

[gneill]

Homework Statement

A parallel plate capacitor with capacitance C is charged to a value q and then isolated. The separation between the plates is then tripled. What was the work required to separate the capacitors?

Homework Equations

U=1/2CV^2
Q=CV
C=ε0A/d

The Attempt at a Solution

W=ΔU=1/2C₁V₁^2-1/2C₂V₂^2
=1/2C*(Q/C)^2-1/2*(C/3)*(Q/C)^2
=Q^2/3C
I tried this but this wasn't the correct answer and I can't figure out why. Thank you in advance for the help

Hi avolp, welcome to Physics Forums.

When you write your formula for ΔU you want to take the final energy and subtract the initial energy. You've got them the other way around, so your answer will be the negative of the correct value.

When you write the energy for the capacitor with the plate separation increased by a factor of 3, be sure to substitute the new capacitance for all the instances of the capacitor value C.

 

[avolp]

Oh okay. Now I understand. Thank you so much.