Electric Field of a Dielectric Sphere

The electric potential in the center of the sphere is equal to the average of the potential at the surface of the sphere, which can be found by integrating the electric field over the surface. In summary, to find the electric potential in the center of a sphere with a uniform charge distribution, use Gauss's Law to find the electric field in the two regions and then integrate the field over the surface to find the potential at the center. The answer is equal to the average of the potential at the surface, which can be found using the electric field.
  • #1
Marvi
2
0

Homework Statement


A uniform charge q is distributed along a sphere of radius R.
a) What is the Electric Potential in the center of the sphere?



Homework Equations


V(r1)-V(r0) = - [tex]\int \stackrel{\rightarrow}{E}[/tex] * [tex]\stackrel{\rightarrow}{dl}[/tex]


The Attempt at a Solution

 
Last edited:
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  • #2
You will need to find the electric field both inside and outside the field and integrate the expression you posted from infinity to R using the field outside and then from R to zero using the field inside.
 
  • #3
Thanks for answering, but actually I can't find the expression for the second part of the Electric field

The first is inside the sphere which leads to [tex]\frac{Kq}{R}[/tex] but the Electric field of the outside part of the sphere I don't know what to do

obs: the answer is : [tex]\frac{6kq}{R}[/tex]
 
  • #4
Use Gauss's Law to find the field in the two regions.
 

1. What is the electric field of a dielectric sphere?

The electric field of a dielectric sphere is the force per unit charge experienced by a charged particle placed at any point inside or outside the sphere. It is affected by the dielectric properties of the material that makes up the sphere.

2. How is the electric field of a dielectric sphere calculated?

The electric field of a dielectric sphere can be calculated using the formula E = Q/(4πεr^2), where E is the electric field, Q is the charge of the sphere, ε is the permittivity of the material, and r is the distance from the center of the sphere.

3. What is the permittivity of a dielectric sphere?

The permittivity of a dielectric sphere is a measure of its ability to store electrical energy in an electric field. It is represented by the symbol ε and is dependent on the material that makes up the sphere.

4. How does the permittivity of a dielectric sphere affect its electric field?

The permittivity of a dielectric sphere affects its electric field by reducing the strength of the electric field inside the sphere. This is due to the polarizing effect of the dielectric material, which creates an opposing electric field that cancels out a portion of the original field.

5. Can the electric field of a dielectric sphere be manipulated?

Yes, the electric field of a dielectric sphere can be manipulated by changing the material of the sphere or by changing the external electric field that is applied to the sphere. By choosing a material with a higher or lower permittivity, the strength of the electric field can be increased or decreased. Additionally, by changing the direction or magnitude of the external electric field, the resulting field inside the sphere can also be altered.

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