Induced polarization for collision between conducting spheres

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.
  • #1
member 731016
Homework Statement
Please see below
Relevant Equations
Please see below
For this part (b) of this problem,
1675050823659.png

The solution is,
1675050872874.png


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!
 
Physics news on Phys.org
  • #2
In what way do you feel it is better?
What do you mean by electrons being polarised?
 
  • Like
Likes member 731016 and nasu
  • #3
haruspex said:
In what way do you feel it is better?
What do you mean by electrons being polarised?
Thanks for your reply @haruspex !

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!
 
  • #4
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.
 
  • Like
Likes member 731016
  • #5
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!
 

FAQ: Induced polarization for collision between conducting spheres

What is induced polarization in the context of conducting spheres?

Induced polarization refers to the redistribution of electric charges within a conducting sphere when it is exposed to an external electric field. In the context of two conducting spheres, this phenomenon occurs when the spheres influence each other's charge distribution due to their proximity, leading to a non-uniform charge distribution on their surfaces.

How does induced polarization affect the collision dynamics between conducting spheres?

Induced polarization affects the collision dynamics by creating attractive or repulsive forces between the spheres. These forces can alter the trajectories and velocities of the spheres, impacting how they collide and separate. The induced charges can lead to complex interactions that are not present in non-conducting or neutral spheres.

What are the mathematical models used to describe induced polarization between conducting spheres?

Mathematical models for induced polarization between conducting spheres typically involve solving Laplace's or Poisson's equations for the electric potential. Boundary conditions are applied to account for the conducting nature of the spheres. Methods such as the method of images, multipole expansion, or numerical simulations like finite element analysis (FEA) are often used to solve these equations and predict the induced charge distributions and resulting forces.

What experimental techniques are used to study induced polarization in conducting spheres?

Experimental techniques to study induced polarization in conducting spheres include using high-precision electrometers to measure surface charge distributions, optical methods such as interferometry to observe changes in electric fields, and high-speed cameras to capture the dynamics of collisions. Additionally, controlled environments with variable electric fields can be used to systematically study the effects of induced polarization.

What are the practical applications of understanding induced polarization in conducting spheres?

Understanding induced polarization in conducting spheres has practical applications in fields such as material science, electronics, and nanotechnology. It can be crucial for designing better capacitors, understanding triboelectric effects, improving electromagnetic shielding, and developing advanced sensors. It also has implications in understanding natural phenomena such as lightning strikes and electrostatic interactions in dust particles.

Back
Top