Analyzing Magnetic Field in a Charged Sphere

In summary, the conversation discusses the concept of a sphere with evenly distributed positive and negative charges in each hemisphere and how to predict the behavior of the electric field at any point inside or outside the sphere. Suggestions for mapping out the field include using the dipole approximation or approximating with a computer.
  • #1
Esran
73
0
Imagine a sphere such that positive charge is evenly distributed throughout one hemisphere (not just on the surface) and equal negative charge is evenly distributed throughout the other hemisphere.

Spherethingy.png


Is there a simple or elegant way to map out the magnetic field inside/outside the sphere and predict the behavior of the field (magnitude, direction) at any arbitrary point inside/outside the sphere?

P.S. Ignore the little plus sign outside the sphere, or better yet, pretend it's a test charge. Also, if you can't make heads or tails of how the sphere would work out, then let me know if you have any ideas how a spherical shell with analogous properties would behave.
 
Physics news on Phys.org
  • #2
(you mean electric field, right? Not magnetic field)
 
  • #3
yeah...that's what lack of sleep does to you.
 
  • #4
I think you could arrive at a simple elegant diagram by doing all the messy work of figuring the electric field between every charge pair and canceling opposing fields to get rid of arrows and clean up the diagram.
 
  • #5
Esran said:
Imagine a sphere such that positive charge is evenly distributed throughout one hemisphere (not just on the surface) and equal negative charge is evenly distributed throughout the other hemisphere.

Spherethingy.png


Is there a simple or elegant way to map out the magnetic field inside/outside the sphere and predict the behavior of the field (magnitude, direction) at any arbitrary point inside/outside the sphere?

P.S. Ignore the little plus sign outside the sphere, or better yet, pretend it's a test charge. Also, if you can't make heads or tails of how the sphere would work out, then let me know if you have any ideas how a spherical shell with analogous properties would behave.

For points external to the sphere and adequately far away (>>R) the (electric) field would be that of an electric dipole. For other distributions, "The Feynman Lectures on Physics", V2, Sect. 6-5 "The dipole approximation for an arbitrary distribution" is suggested reading. For external points up close to the spherical surface, and/or for points internal to the sphere, I don't know. I'd be inclined to approximate E using a computer.
 

FAQ: Analyzing Magnetic Field in a Charged Sphere

What is a charged sphere?

A charged sphere is a spherical object that has an electric charge. This charge can be either positive or negative, and it is evenly distributed on the surface of the sphere.

Why is it important to analyze the magnetic field in a charged sphere?

Analyzing the magnetic field in a charged sphere allows us to understand the behavior of charged particles within the sphere. This is important in many applications, such as in the design of electronic devices or in studying the behavior of charged particles in space.

How is the magnetic field in a charged sphere calculated?

The magnetic field in a charged sphere can be calculated using the formula B = μ0 * (Q * v * r)/ (4 * π * R^3), where B is the magnetic field, μ0 is the permeability of free space, Q is the charge of the sphere, v is the velocity of the charged particle, r is the distance from the center of the sphere, and R is the radius of the sphere.

What factors affect the strength of the magnetic field in a charged sphere?

The strength of the magnetic field in a charged sphere is affected by several factors, including the charge of the sphere, the velocity of the charged particle, and the distance from the center of the sphere. Additionally, the permeability of free space and the radius of the sphere also play a role in determining the strength of the magnetic field.

How does the direction of the magnetic field in a charged sphere change?

The direction of the magnetic field in a charged sphere changes as the position of the charged particle within the sphere changes. The magnetic field lines always point in the direction that the charged particle is moving, and they form concentric circles around the particle's path. As the particle moves closer to the center of the sphere, the direction of the magnetic field lines becomes more perpendicular to the particle's path.

Similar threads

B Can charges move without a field? How charges redistribute without it?
Replies
16
Views
919
I Average field inside spherical shell of charge
Replies
3
Views
790
I Why is the E-field inside a solid conducting sphere zero?
Replies
4
Views
2K
Induced charge on a conducting sphere sliced by a plane
Replies
2
Views
627
Magnetization of a paramagnetic sphere
Replies
11
Views
644
I Electrostatic force exerted on an electron inside a nucleus
Replies
19
Views
1K
Electric field external to Conducting Hollow Sphere with charge inside
Replies
23
Views
2K
I Solving Gauss' Law Problem: Zero E Field?
Replies
34
Views
3K
I Charging a small metal ball from a charged hollow sphere
Replies
4
Views
404
I Electric field inside & outside of a spherical shell
Replies
7
Views
307

Hot Threads

Recent Insights

Back
Top