E-field from uniformly distributed charges on sphere?

In summary, for a sphere of uniform charge distribution, the electric field at a point away from the sphere is affected by all individual charges distributed across the sphere and the net effect is only in the X direction due to equal opposing forces in the Y and Z directions. This can also be calculated using Coulomb's law and Gauss's Law, and the results will match due to Newton's shell theorem.
  • #1
yosimba2000
206
9
So if I have a sphere of uniform charge distribution, the electric field at one point away from the circle would be affected by ALL individual charges distributed across the circle, right?

From the picture I drew, there would only be a net effect of E-field in the X direction because there would be equal opposing forces in the Y-direction as well as Z-direction, right?

If I added up all the electric fields in the X-direction at that point using Coulomb's law for each point charge on the sphere, would it also match the E-field calculated from Gauss's Law?

I've drawn a top-down picture here: https://imgur.com/a/kAQjS
 
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  • #2
yosimba2000 said:
I've drawn a top-down picture here: https://imgur.com/a/kAQjS

In future always try and post images to the thread ... It's much easier for people to discuss the query :smile: ...

Vh1nr8S.gif


there we go :wink:
 
  • #3
is the sphere hollow or solid ?
Is point P a charge or are you just wanting to know what the E-field is at that point ?

for a Gaussian hollow sphere have you come across this in your studies ? ...

upload_2017-10-9_15-30-45.png
Dave
 
  • #4
yosimba2000 said:
So if I have a sphere of uniform charge distribution, the electric field at one point away from the circle would be affected by ALL individual charges distributed across the circle, right?
Yes
yosimba2000 said:
From the picture I drew, there would only be a net effect of E-field in the X direction because there would be equal opposing forces in the Y-direction as well as Z-direction, right?
Yes, so long as the center of the sphere and point p are both on the x axis.
yosimba2000 said:
If I added up all the electric fields in the X-direction at that point using Coulomb's law for each point charge on the sphere, would it also match the E-field calculated from Gauss's Law?
yes, this is a result of Newton's shell theorem https://en.wikipedia.org/wiki/Shell_theorem.
 

1. What is an E-field from uniformly distributed charges on a sphere?

The E-field from uniformly distributed charges on a sphere is a measure of the electric field strength at any point in space surrounding a sphere that has a uniform distribution of electric charges on its surface. This field is created by the electric charges on the surface of the sphere and is responsible for the electric force experienced by other charges in its vicinity.

2. How is the E-field calculated from uniformly distributed charges on a sphere?

The E-field from uniformly distributed charges on a sphere can be calculated using the formula E = kQ/r^2, where E is the electric field strength, k is the Coulomb's constant, Q is the total charge on the sphere, and r is the distance from the center of the sphere to the point where the field is being measured.

3. What is the direction of the E-field from uniformly distributed charges on a sphere?

The direction of the E-field from uniformly distributed charges on a sphere is radial, meaning it points away from or towards the center of the sphere depending on the sign of the charges. If the charges are positive, the field points away from the center, and if the charges are negative, the field points towards the center.

4. How does the E-field from uniformly distributed charges on a sphere change with distance?

The E-field from uniformly distributed charges on a sphere follows an inverse square law, which means that as the distance from the center of the sphere increases, the field strength decreases. This is because the electric charges are spread out over a larger area, resulting in a weaker field at a greater distance.

5. What are some real-life applications of the E-field from uniformly distributed charges on a sphere?

The E-field from uniformly distributed charges on a sphere has many real-life applications, such as in electrostatic painting, where the E-field is used to attract paint particles towards a surface. It is also used in electrostatic precipitators to remove pollutants from industrial exhaust gases. Additionally, the E-field is used in particle accelerators to control the motion of charged particles.

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