# Induced polarization for collision between conducting spheres

• ChiralSuperfields
In summary, the solution to part (b) of this problem involves the concept of conductors and their free electrons being polarized by an external electric field. This results in a decrease in the effective distance between the centers of charge, causing the spheres to be closer together and converting more electric potential energy to kinetic energy. There is a discrepancy in the explanations provided, with one mentioning the field and the other mentioning the movement of electrons on the surface of the spheres. Additionally, the reference to the "insides" of the spheres is ambiguous and could be clarified.

#### ChiralSuperfields

Homework Statement
Relevant Equations
For this part (b) of this problem,

The solution is,

However, would a better explanation be:

As the spheres are conductors, there will be free electrons within and on the surface of the conductors that will be polarized by the external electric field between the conductor. This will decrease the effective distance between the centers of charge (won't affect net charge of sphere; only where charge is distributed locally within the sphere). Therefore, the spheres will be closer together that ##r_1 + r_2## so more electric potential energy will be converted to kinetic energy.

Thank you!

In what way do you feel it is better?
What do you mean by electrons being polarised?

ChiralSuperfields and nasu
haruspex said:
In what way do you feel it is better?
What do you mean by electrons being polarised?

I guess their solution sort of implies that the surface becomes polarized due to the electric field between the spheres. While mine, at least tried too, said that surface will become polarized due to the movement of the electrons local to the surface.

Sorry yes I now realize that I said electrons become polarized, I meant the surface. Electrons can't get polarized since they already have a finite charge ##-e## in a uniform sphere.

Many thanks!

Callumnc1 said:
their solution sort of implies that the surface becomes polarized due to the electric field between the spheres. While mine, at least tried too, said that surface will become polarized due to the movement of the electrons local to the surface.
Reaaly? Their explanation says nothing about the field and does not use the word "polarised" but does say the electrons move - without saying why.
What I don't like is the reference to the "insides" of the spheres. Too ambiguous. I would have said that on each sphere they move to the side facing the other sphere.

ChiralSuperfields
haruspex said:
Reaaly? Their explanation says nothing about the field and does not use the word "polarised" but does say the electrons move - without saying why.
What I don't like is the reference to the "insides" of the spheres. Too ambiguous. I would have said that on each sphere they move to the side facing the other sphere.
Thank you for your reply @haruspex ! I like what you pointed out about the insides of the spheres!