Fields of Rotating Dielectric Sphere in Dielelectric Medium

[TeslaCoil137]

Homework Statement

A dielectric sphere with the electric and magnetic susceptibilities ε1 and µ1 is rotating with angular frequency ω in a constant electric field E~ in a medium, characterized by the parameters ε2 and µ2. The angle between the rotation axis and the direction of E~ is α. Find the electric and magnetic fields inside the sphere and in the medium

Homework Equations

Minkowski Relations: D = ε1*E +(ε1μ1 -1)*(ωxr)xH; B =µ1H -(ε1µ1 -1)*(ωxr)xE
Maxwell Equations
Electric field of at rest sphere in vacuum with applied E field: 3/(ε1 +2) *Ecosα

The Attempt at a Solution

If this was in vacuum I could straightforwardly apply the Minkowski relations as in, say Jackson Problem 6.8, But I don't know how to account for the dielectric medium itself.

 

[mark726]

you would first need to understand the properties of dielectric materials and how they interact with electric and magnetic fields. Dielectric materials have the ability to store electric charge and are characterized by their dielectric constant (ε) and magnetic permeability (µ). In this case, the dielectric sphere is rotating in a medium with different ε and µ values, which will affect the electric and magnetic fields inside the sphere and in the medium.

To solve this problem, you could start by using the Maxwell equations to find the electric and magnetic fields inside the sphere and in the medium. These equations relate the electric and magnetic fields to the charge and current densities in the medium. In this case, the charge and current densities will be affected by the dielectric properties of the medium.

Next, you could use the Minkowski relations to find the relationship between the electric and magnetic fields inside the sphere and in the medium. These relations take into account the effects of the dielectric properties of the medium on the electric and magnetic fields.

Finally, you could use the electric field formula for a sphere at rest in vacuum to find the electric field inside the sphere. This formula takes into account the dielectric constant of the sphere and the angle between the rotation axis and the direction of the electric field.

Overall, solving this problem will require a thorough understanding of dielectric materials and their interactions with electric and magnetic fields. It may also be helpful to consult other resources or seek guidance from colleagues or experts in the field.