Find the electric field of a point outside sphere

In summary, the conversation discusses finding the electric field of a point outside a spherical shell without using Gauss's law. Coulomb's law and the spherical coordinate system are mentioned as relevant equations. The attempt at a solution involves expressing the distance from the point to the differential element in terms of other variables, with consideration for the symmetry of the problem. The type of sphere, whether imaginary, solid, conducting, or grounded, is also mentioned as a relevant factor in finding a solution. The method of images is suggested as a possible approach for a conducting sphere.
  • #1
Coderhk
59
2

Homework Statement


Find the electric field of a point outside sphere without using Gauss's law. (Do not evaluate the integral)

Homework Equations


Coulomb's Law
Spherical Co-ordinate System

The Attempt at a Solution


I have attached my attempt as a picture but now I am stuck, I don't know how I can express the distance (h )from the point to the differential element in terms of the other variables. From symmetry I know the y component of the electric field will cancel out
 

Attachments

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  • #2
Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?
 
  • #3
BvU said:
Mission impossible without a complete problem statement: what kind of sphere ? Imaginary, solid, conducting, grounded ?
I believe the question is talking about a shpherical shell like a gaussian enclosed sphere. I figured out that I need to express h in terms of the cos law. Thanks.
 
  • #4
Conducting ? In which case the method of images might help ...
 

1. What is the formula for finding the electric field of a point outside a sphere?

The formula for finding the electric field of a point outside a sphere is E = kQ/r^2, where E is the electric field, k is the Coulomb's constant, Q is the charge of the sphere, and r is the distance between the point and the center of the sphere.

2. How do you determine the direction of the electric field outside a sphere?

The direction of the electric field outside a sphere is always away from the center of the sphere, in a radial direction. This means that the electric field lines will point outward from the sphere.

3. Can the electric field outside a sphere be negative?

Yes, the electric field outside a sphere can be negative if the charge of the sphere is negative. This indicates that the electric field is directed towards the center of the sphere instead of away from it.

4. What is the relationship between the electric field and the distance from a point outside a sphere?

The electric field outside a sphere is inversely proportional to the square of the distance from the point to the center of the sphere. This means that as the distance increases, the electric field decreases.

5. How does the electric field outside a conducting sphere differ from that of a non-conducting sphere?

The electric field outside a conducting sphere is the same as that of a point charge located at the center of the sphere. In contrast, the electric field outside a non-conducting sphere is affected by the distribution of charge within the sphere, and may vary at different points outside the sphere.

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