How much charge on a plate needed to lift it against gravity?

[bjnartowt]

Homework Statement

A thin uniform metal disk lies on an infinite conducting plane. A uniform gravitational field is oriented normal to the plane. Initially the disk and plane are uncharged; charge is slowly added. The mass of the disk is M, and its area is A. What value of charge density is required to cause the disk to leave the plate?

Homework Equations

The Attempt at a Solution

see attachment. The question I have: why did my professor tell me "Consider doing some virtual work over distance (dW/dx is kind of like a force), add gravity, and set it equal to zero." This implied I should find the potential everywhere. But I don't see how finding the potential everywhere (with an image-disk) would help, since that would be the potential felt by an observer, *not* the real disk itself. I think my approach is best. And that's when I get extra worried: if my approach is convincing to no one but me, 'cuz that means I'm *really* missing something...

 

[mark726]

Your professor may have suggested finding the potential everywhere because it can provide insight into the behavior of the disk as it gains charge. By considering the potential, you can see how it changes as charge is added and how it affects the disk's motion.

However, your approach of using virtual work and setting it equal to zero is also valid. It takes into account the forces acting on the disk and determines the necessary charge density to overcome those forces and cause the disk to leave the plate.

It is important to consider both approaches and see how they complement each other in understanding the problem. I would suggest discussing this further with your professor to gain a better understanding of the concepts involved.

Best of luck with your studies!