Electrostatic field of a sphere

In summary, the conversation discusses the electrostatic field of a non-conductive sphere with a density charge distribution inside. Parameters for this sphere include ρ0 and R. Gauss's law is used to solve for the electric field in two regions of space, with different functional dependence for the field. The field is found for one region, but not the other. Further clarification and simplification may be needed.
  • #1
gebhaard
1
0
Homework Statement
What is the electrostatic field of a non-conductive sphere (it's radius is R) which has a density charge distribution inside? ρ0 and R are parameters.
Relevant Equations
Gauss' law
What is the electrostatic field of a non-conductive sphere (it's radius is R) which has a
1585772034040.png

density charge distribution inside? ρ0 and R are parameters.

I started solving this with Gauss's law:
1585771866519.png

then:
1585771887327.png

Solving the integral:
1585771903343.png

This means the electrostatic field of the sphere in r is:
1585771919260.png


Can you check if is this correct? If it isn't, what is the problem?
Thanks.
 
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  • #2
Can you not simplify that answer? Also, the electric field is a vector.
 
  • #3
Also, there are two regions in space with different functional dependence for the field, ##r'<R## and ##r' \geq R##. You found the field in the former but not the latter.
 

1. What is the formula for calculating the electrostatic field of a sphere?

The formula for calculating the electrostatic field of a sphere is E = kQ/r^2, where E is the electric field, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the charge of the sphere, and r is the distance from the center of the sphere.

2. How does the electrostatic field of a sphere vary with distance?

The electrostatic field of a sphere follows an inverse square law, meaning that it decreases as the distance from the center of the sphere increases. This means that the closer you are to the sphere, the stronger the electric field will be.

3. Does the size of the sphere affect the strength of the electrostatic field?

Yes, the size of the sphere does affect the strength of the electrostatic field. The larger the sphere, the greater the charge and therefore the stronger the electric field. However, the distance from the center of the sphere also plays a role in determining the strength of the field.

4. How does the charge of the sphere affect the electrostatic field?

The charge of the sphere directly affects the strength of the electrostatic field. The greater the charge, the stronger the field will be. Additionally, the direction of the field will depend on the polarity of the charge (positive or negative).

5. What is the significance of the electrostatic field of a sphere in real-world applications?

The electrostatic field of a sphere has many real-world applications, including in electrostatic painting, electrostatic precipitation (used in air pollution control), and in the design of capacitors and other electrical devices. Understanding the electrostatic field of a sphere is also important in understanding the behavior of charged particles in electric fields.

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