Problem with solving laplace equation with a charged ring

In summary, for the given situation of a ring charge of total charge Q and radius a concentric with a grounded conducting sphere of radius b (<a) in the equatorial plane, the potential is 0 for r < b and Q/4πε for b < r < a. The method of images may be used to determine the potential everywhere in 3D.
  • #1
throwaway128
2
0

Homework Statement


A ring charge of total charge Q and radius a is concentric with a grounded conducting sphere of radius b, b < a.
Determine the potential everywhere. The ring is located in the equatorial plane, so both the sphere and the ring have their center at the same spot.

Homework Equations


∇V=0

The Attempt at a Solution


Well the region r < b is V = 0.
At first I thought about using the Laplace equatio for he next zone (b < r < a) making it zero on the surface of the sphere and Q/4πε on the ring, but then I am at a draw and don't know what to do next.
 
Physics news on Phys.org
  • #2
throwaway128 said:
Determine the potential everywhere.
Everywhere in 3D, or just in the equatorial plane?
 
  • #3
throwaway128 said:
Q/4πε on the ring,
Don't forget the induced charge on the sphere.
 
  • #4
haruspex said:
Everywhere in 3D, or just in the equatorial plane?
It is everywhere in 3D.
 
  • #5
This one looks beyond me. The method of images might be applicable.
 

1. What is the Laplace equation?

The Laplace equation is a partial differential equation that describes the behavior of a scalar function in a given space. It is used to solve a variety of physical problems, including electrostatics and fluid dynamics.

2. What is a charged ring?

A charged ring is a circular object that has a net electric charge. This charge may be positive or negative, and it can interact with other charged particles in its surrounding environment.

3. What is the problem with solving the Laplace equation for a charged ring?

The problem with solving the Laplace equation for a charged ring is that it is a boundary value problem, meaning that the solution depends on the values of the function on the boundaries of the given space. In the case of a charged ring, the boundary conditions are complex and can make the problem difficult to solve analytically.

4. How is the Laplace equation usually solved for a charged ring?

The Laplace equation for a charged ring is typically solved using numerical methods, such as the finite element method or the boundary element method. These methods involve discretizing the problem into smaller, more manageable parts and using algorithms to find an approximate solution.

5. What are some applications of solving the Laplace equation for a charged ring?

Solving the Laplace equation for a charged ring has many practical applications, including in the design of electrical circuits, antennas, and other electronic devices. It is also used in the study of fluid dynamics, as the electric field created by the charged ring can influence the motion of charged particles in a fluid.

Similar threads

Hall effect over a conducting ring
    • Introductory Physics Homework Help
Replies
4
Views
875
What's wrong? Electric potential of a point on a ring
    • Introductory Physics Homework Help
Replies
10
Views
1K
Electric field external to Conducting Hollow Sphere with charge inside
    • Introductory Physics Homework Help
Replies
17
Views
411
Derivation of electric potential charged disk from ring
    • Introductory Physics Homework Help
Replies
6
Views
1K
Electric field of concentric rings
    • Introductory Physics Homework Help
Replies
2
Views
3K
Electric field of ring of charge/washer of charge/disk of charge
    • Introductory Physics Homework Help
Replies
9
Views
3K
Several questions relating to work, electric potential energy, and potential difference
    • Introductory Physics Homework Help
Replies
22
Views
1K
I Question regarding Laplace's Equation for regions with charges
    • Electromagnetism
Replies
11
Views
855
Three charges constrained to a ring
    • Introductory Physics Homework Help
Replies
4
Views
891
Conceptual Laplace's/Poisson's Equation Solution Questions
    • Introductory Physics Homework Help
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top