Electric field of a spherical cap

In summary, the electric field of a spherical cap is a vector quantity that represents the force per unit charge acting on a charged particle at any point along the surface of the cap. It can be calculated using the formula E = (Q/4πε₀)(1/r² - 1/R²), and is affected by factors such as the charge and radius of the cap, as well as the surrounding medium. It can be negative, and is similar to the electric field of a point charge but may differ in strength and direction based on the charge distribution of the cap.
  • #1
Gavroy
235
0
Hi

I am looking for the electric field caused by a uniformly charged spherical cap.
Actually, I need only the potential inside the sphere. Is there anybody who knows how to do this. Frankly, I do not have a clue. Or could somebody at least give me integral, that I have to solve?
 
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  • #2
You can find the solution here: http://faculty.uml.edu/cbaird/all_homework_solutions/Jackson_3_2_Homework_Solution.pdf . Apparently one needs Legendre polynomials to represent the solution.
 

What is the electric field of a spherical cap?

The electric field of a spherical cap is the force per unit charge acting on a charged particle at any point along the surface of the cap. It is a vector quantity and its direction is determined by the direction of the force on a positive test charge.

How is the electric field of a spherical cap calculated?

The electric field of a spherical cap can be calculated using the formula E = (Q/4πε₀)(1/r² - 1/R²), where Q is the charge of the spherical cap, ε₀ is the permittivity of free space, r is the distance from the center of the spherical cap to the point of interest, and R is the radius of the spherical cap.

What factors affect the electric field of a spherical cap?

The electric field of a spherical cap is affected by the charge of the cap, the distance from the center of the cap to the point of interest, and the radius of the cap. It is also influenced by the medium surrounding the cap, as the permittivity of the medium can alter the strength of the electric field.

Can the electric field of a spherical cap be negative?

Yes, the electric field of a spherical cap can be negative. This indicates that the force on a positive test charge at that point would be in the opposite direction as the field. This can occur if the charge of the cap is negative or if the charge distribution is not uniform.

How does the electric field of a spherical cap compare to that of a point charge?

The electric field of a spherical cap can be thought of as a combination of multiple point charges, with each small element of the cap acting as a point charge. As a result, the electric field of a spherical cap is similar to that of a point charge, but may differ in strength and direction depending on the charge distribution of the cap.

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