Electrostatics || A cone charged unifomly, find intensity

In summary, the problem involves finding the electrostatic field intensity at the top of a cone with a uniform charge distribution. The formula for this is E=ρ/(4πε0) ∫Ω dΩ/R2) and can be solved using cylindrical coordinates. The steps to do so can be found online.
  • #1
Ciumko
4
0

Homework Statement


A cone of height H and base radius A is charged with charge Q uniformly distributed in all its volume. Find electrostatic field intensity at the top of the cone.

DATA: H, A, Q

Homework Equations


E=ρ/(4πε0) ∫Ω dΩ/R2)

and R is a vector (rr^+zz^) r^ and z^ are versors

The Attempt at a Solution


Don't have idea how to integrate this, hope anyone can help me.
 
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  • #2
Use cylindrical coordinates. This gives you a triple integral.
 
  • #3
How do I do this?
 
  • #4
Ciumko said:
How do I do this?
Are you familiar with cylindrical coordinates?
Do you know how to write an integral over a volume using such?
Both topics can be easily found on the net.
 

1. What is electrostatics?

Electrostatics is a branch of physics that deals with the study of electric charges at rest.

2. How is intensity defined in electrostatics?

Intensity is a measure of the strength of an electric field at a particular point, and is defined as the force per unit charge exerted on a test charge placed at that point.

3. What is a uniformly charged cone?

A uniformly charged cone is a three-dimensional shape with a pointy end and a circular base, where the electric charge is distributed evenly throughout the surface of the cone.

4. How do you calculate the intensity of a cone charged uniformly?

To calculate the intensity of a cone charged uniformly, you can use the formula I = Q/(4πεr²), where I is the intensity, Q is the charge on the cone, ε is the permittivity of the medium, and r is the distance from the apex of the cone to the point at which intensity is being calculated.

5. Can the intensity of a cone charged uniformly be negative?

No, the intensity of a cone charged uniformly cannot be negative. It is always positive and represents the magnitude of the electric field at a particular point.

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