Finding E and B field of a weird charge distribution

In summary, the conversation discusses a problem involving a spherical charge distribution and the expansion of its radius over time. The problem also involves finding the charge density, current density, E-field, and B-field, using the 4 Maxwell equations and the continuity equation. The person has already computed ρ, J, and E, and is seeking help with solving Ampere's Law with Maxwell Correction.
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Homework Statement


Initially there is a spherical charge distribution of with a radius ##R_0## and uniform charge density ##ρ_0##. Suppose the distribution expands spherically symmetrically such that its radius at time t is ##R_0 + V t##, where V is the velocity. Assuming the density remain uniform inside the sphere as time increases, find the charge density and current density,E-field and B-field

Homework Equations


4 maxwell equations and continuity equation

The Attempt at a Solution


I have computed ##ρ## and ##J##, so does E. I want to know if ##J=ρV## in r direction.Then I find that curl of E=0, which means B is independent of time, which is strange. And I find it very complicated to solve the Ampere's Law with Maxwell Correction.
Any hints? Thank you
 
Physics news on Phys.org

1. How do I find the E and B fields of a weird charge distribution?

To find the electric and magnetic fields of a weird charge distribution, you can use the principles of electromagnetism. Start by calculating the electric field using Coulomb's law or Gauss's law, depending on the geometry of the distribution. Then, use the Biot-Savart law to find the magnetic field.

2. What is a weird charge distribution?

A weird charge distribution is any non-traditional arrangement of charged particles that does not have a simple geometric shape, such as a point charge or a uniform line or surface charge. Examples of weird charge distributions could include multiple point charges at varying distances, charged particles arranged in a spiral, or a combination of different charge distributions.

3. How is a weird charge distribution different from a traditional one?

A traditional charge distribution, such as a point charge or a uniform line/surface charge, has a simple geometric shape that allows for straightforward calculations of the electric and magnetic fields. In contrast, a weird charge distribution does not have a simple shape and may require more complex calculations to determine the fields.

4. Can I use superposition to find the E and B fields of a weird charge distribution?

Yes, you can use the principle of superposition to find the electric and magnetic fields of a weird charge distribution. This principle states that the total field at a point due to multiple charges is equal to the vector sum of the individual fields from each charge.

5. Are there any approximations or simplifications that can be made when finding the E and B fields of a weird charge distribution?

Yes, there are some approximations and simplifications that can be made when dealing with a weird charge distribution. For example, if the distribution is symmetric, you can use symmetry arguments to simplify the calculations. Additionally, in some cases, you can approximate the distribution as a collection of point charges or a continuous charge distribution to make the calculations easier.

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