Electric force between two spheres

In summary, the conversation discusses the question of whether the sphere of radius 'a' can be modeled as a point particle, given that it has a non-uniform charge distribution. The upper sphere, with a uniform charge, can be modeled as a point particle. However, it is not possible to model the lower sphere as a point particle due to its non-uniform charge distribution.
  • #1
Abwi
1
0

Homework Statement



Captura.png

[/B]
Find the electric force between the two spheres.
Sphere r=b-a has a volumetric density of p=K, where K is a constant
Sphere r=a has a volumetric density of p=θ*r

Homework Equations


As you can see the sphere of radius 'a' doesn't have a uniform electric field because it varies with respect to 'θ' and 'r'. I need to know if the sphere of radius 'a' can be modeled as a point particle even if isn't uniformly charged?

The Attempt at a Solution


[/B]
The upper sphere can be modeled as a point particle because it is uniformly charged so I can obtain its charge which is Q =
Captura3.png


For the sphere centered at the origin I define an r vector between a point P inside the sphere of radius a in respect to the center of the upper sphere. Which after some arrangements leaves me with this expression for it's electric displacement field D =
Captura2.png

This field goes on the positive z direction.

And this integral cannot be solved analytically as far as I know. Which is why I want to know if that sphere can be modeled as a point particle so I can just multiply the charges of each sphere?
 
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  • #2
Abwi said:
I need to know if the sphere of radius 'a' can be modeled as a point particle even if isn't uniformly charged?
Hi Abwi:

It has been a very long time since I was into this topic, but I am pretty sure the answer to the above question is NO. It may be possible for a non-uniform charge distribution over a spherical surface to be equivalent to all the charge at the center, but in such case the distribution would have to have certain symmetries. However since the upper sphere has uniform charge, its force w/r/t other charged sources is the same as if it were a point charge at its center. If the lower sphere's distribution is symmetric w/r/t the line connecting the two centers, the the lower sphere's force on the upper sphere would be the same as if it were a point charge at some point on this line, but not necessarily the center of the lower sphere.

Hope this helps.

Regards,
Buzz
 
  • #3
Is θ the polar or azimuth angle (latitude or longitude)?
 

What is the electric force between two spheres?

The electric force between two spheres is a measure of the attraction or repulsion between the two spheres due to their electric charges. It is governed by Coulomb's Law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between the spheres.

How is the electric force between two spheres calculated?

The electric force between two spheres can be calculated using the equation F = k * (q1 * q2) / r^2, where F is the force, k is the Coulomb's constant, q1 and q2 are the charges of the spheres, and r is the distance between them.

What factors affect the electric force between two spheres?

The electric force between two spheres is affected by the magnitude of the charges on the spheres, the distance between them, and the medium they are in. In a vacuum, the force is only affected by the charges and the distance. In a medium, the force is also affected by the medium's dielectric constant.

What is the direction of the electric force between two spheres?

The direction of the electric force between two spheres depends on the charges of the spheres. If the charges are of the same sign, the force will be repulsive and in the opposite direction of the line connecting the two spheres. If the charges are of opposite signs, the force will be attractive and in the direction of the line connecting the two spheres.

How does the electric force between two spheres compare to the gravitational force?

The electric force between two spheres is much stronger than the gravitational force between them. This is because the electric force is proportional to the product of the charges, which can be much larger than the masses involved in gravitational forces. Additionally, the electric force can be attractive or repulsive, while the gravitational force is always attractive.

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