- #1

lys04

- 70

- 3

- Homework Statement
- Several questions relating to work, electric potential energy, and potential difference.

- Relevant Equations
- kq1q2/r

kq/r

I have several questions relating to electrostatics:

first of all, in this derivation for the formula of the electric potential energy:

work is being done against the electric field right, so the work should be negative, but in this case it's positive. I'm wondering if it's because the direction of dr and the force should be in the same direction so when you take the dot product it's a positive result? Then the work done will be negative and according to the equation W=-delta U then U will be equal to positive kq1q2/r?

Second question, the equation V=kq/r can only be used on point charges right since it comes from V=U/q and the equation for U comes from work which involves Coulomb's law, which only applies for point charges.

Third question, why is the potential difference for a spherical conductor at the surface kq/r? This relates to my question above, how can the spherical conductor be assumed to be a point charge at the surface?

Last question, why is the potential difference inside the spherical conductor not 0 if there is no electric field? Also, I saw some posts saying that the potential difference inside is equal to that on the surface because there is no electric field inside and so there is no work done, so the difference in potential is 0 and hence Vinside=Vsurface. But the surface isn't INSIDE the sphere anymore? Or am I just overthinking it?

first of all, in this derivation for the formula of the electric potential energy:

work is being done against the electric field right, so the work should be negative, but in this case it's positive. I'm wondering if it's because the direction of dr and the force should be in the same direction so when you take the dot product it's a positive result? Then the work done will be negative and according to the equation W=-delta U then U will be equal to positive kq1q2/r?

Second question, the equation V=kq/r can only be used on point charges right since it comes from V=U/q and the equation for U comes from work which involves Coulomb's law, which only applies for point charges.

Third question, why is the potential difference for a spherical conductor at the surface kq/r? This relates to my question above, how can the spherical conductor be assumed to be a point charge at the surface?

Last question, why is the potential difference inside the spherical conductor not 0 if there is no electric field? Also, I saw some posts saying that the potential difference inside is equal to that on the surface because there is no electric field inside and so there is no work done, so the difference in potential is 0 and hence Vinside=Vsurface. But the surface isn't INSIDE the sphere anymore? Or am I just overthinking it?