Electrodynamics, Potentials, spherical uncharged shells

In summary, the problem is to find the potential inside an uncharged spherical shell of finite width using the Laplace principle. The shell is placed in an electric field in the z-axis direction. The equation for potential is called the 2-D Laplace's equation, where u represents potential. By using spherical coordinates and applying the Dirichlet boundary conditions, two separate differential equations are obtained. The solution to these equations depends on an integer, which can be summed over to obtain a general solution.
  • #1
Dealingwithphysics
2
0

Homework Statement


using Laplace principle find potential inside an uncharged spherical shell of finite width. shell is placed in an electric field E in z-axis direction.

Homework Equations


eq0001M.gif
in this equation u is potential. equation is called 2-D Laplace’s equation.

The Attempt at a Solution


diagram which i picture in my mind is like as under.

[/B]
 

Attachments

  • eq0001M.gif
    eq0001M.gif
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  • #2
Dealingwithphysics said:

Homework Statement


using Laplace principle find potential inside an uncharged spherical shell of finite width. shell is placed in an electric field E in z-axis direction.

Homework Equations


View attachment 217586 in this equation u is potential. equation is called 2-D Laplace’s equation.

The Attempt at a Solution


diagram which i picture in my mind is like as under.

[/B]
please don't delete i don't have further info related to problem. its it.
 
  • #3
Dealingwithphysics said:
3. The Attempt at a Solution
diagram which i picture in my mind is like as under.

Dealingwithphysics said:
please don't delete i don't have further info related to problem. its it.
Your image did not Upload correctly. As you know, we cannot provide tutorial help until you show us your best efforts to work the problem. Please try again to Upload a JPEG or PDF image of your work, or just type your work into the forum window using the math symbols under the sigma ∑ symbol, or use LaTeX (see the tutorial under INFO at the top of the page, Help/How-To). Thank you.
 
  • #4
First is preferably to use spherically coordinates for our two-dimensional
Laplacian. Then you can separate the
variables and actually obtain two different (simple) differential equations.
Upon obeying the Dirichlet boundary conditions you obtain a particular solution depending on an integer.
Then you sum over all values of those
integer numbers in order to obtain a general solution.
so
 

What is Electrodynamics?

Electrodynamics is the branch of physics that deals with the study of electromagnetic fields and their interactions with charged particles. It is based on Maxwell's equations, which describe how electric and magnetic fields are generated and how they influence each other.

What are Potentials in Electrodynamics?

Potentials in Electrodynamics refer to the electric and magnetic potential fields, which are scalar and vector quantities, respectively. They are used to describe the strength and direction of the electric and magnetic fields at a given point in space. The potential fields are related to the electric and magnetic fields through mathematical equations.

What is a Spherical Uncharged Shell?

A spherical uncharged shell is a hypothetical object in electromagnetism that has no net charge and has a spherical shape. This means that the electric field inside the shell is zero, and there is no electric force on any charged particles inside the shell. However, the electric field outside the shell can still be affected by the distribution of charges on the surface of the shell.

How does a Spherical Uncharged Shell affect Electric Potential?

A spherical uncharged shell does not affect the electric potential inside the shell, as the electric field is zero. However, the shell can have an effect on the electric potential outside the shell. If the shell has a uniform distribution of charge on its surface, it can create a constant electric potential on the outside. If the shell has a non-uniform distribution of charge, the electric potential outside will vary depending on the location.

What are some real-world applications of Electrodynamics and Potentials?

Electrodynamics and Potentials have numerous real-world applications, including electromagnets used in motors and generators, electromagnetic radiation used in communication technology, and the study of electric fields in living organisms. They also play a crucial role in understanding and predicting phenomena such as lightning, auroras, and the behavior of charged particles in space.

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