- #1

insomniac392

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Hello,

I've been extremely stuck on the following problems and was hoping someone could give me a push in the right direction:

1) Given an infinite slab of permanently magnetized matter of thickness d centered on the xy-plane with uniform magnetization [tex]\textbf{M} = (0, M, 0)[/tex] and velocity [tex]\textbf{v} = (v, 0, 0)[/tex], find the electric field at [tex]\textbf{E}(0, 0, 0)[/tex] and [tex]\textbf{E}(0, y, 0)[/tex] where y > d.

2) A magnetized sphere with uniform magnetization [tex]\textbf{M} = (0, 0, M)[/tex] and radius r is spinning at a rate of [tex]\textbf{\omega} = (0, 0, \omega)[/tex]. Find the electric field for r' > r. (Hint: Find the equivalent magnetic charge density, [tex]\rho_m[/tex], and equivalent surface current, [tex]\sigma_m[/tex].)

I'm not entirely sure (hence the thread)!

[tex]\sigma_{m, n} = \textbf{M} \cdot \textbf{n}[/tex]

[tex]\rho_{m} = - \nabla \cdot \textbf{M}[/tex]

...these are factors of the integrand that give rise to the magnetic scalar potential, [tex]\Omega[/tex], which in turn yields [tex]\textbf{B}[/tex] via [tex]\textbf{H} = - \nabla \Omega[/tex].

I'm desperately stuck on these; for both problems I can find [tex]\rho_m[/tex] and [tex]\sigma_m[/tex], but I don't see the connection to the [tex]\textbf{E}[/tex]-field. Any suggestions to get me started would be greatly appreciated.

I've been extremely stuck on the following problems and was hoping someone could give me a push in the right direction:

## Homework Statement

1) Given an infinite slab of permanently magnetized matter of thickness d centered on the xy-plane with uniform magnetization [tex]\textbf{M} = (0, M, 0)[/tex] and velocity [tex]\textbf{v} = (v, 0, 0)[/tex], find the electric field at [tex]\textbf{E}(0, 0, 0)[/tex] and [tex]\textbf{E}(0, y, 0)[/tex] where y > d.

2) A magnetized sphere with uniform magnetization [tex]\textbf{M} = (0, 0, M)[/tex] and radius r is spinning at a rate of [tex]\textbf{\omega} = (0, 0, \omega)[/tex]. Find the electric field for r' > r. (Hint: Find the equivalent magnetic charge density, [tex]\rho_m[/tex], and equivalent surface current, [tex]\sigma_m[/tex].)

## Homework Equations

I'm not entirely sure (hence the thread)!

[tex]\sigma_{m, n} = \textbf{M} \cdot \textbf{n}[/tex]

[tex]\rho_{m} = - \nabla \cdot \textbf{M}[/tex]

...these are factors of the integrand that give rise to the magnetic scalar potential, [tex]\Omega[/tex], which in turn yields [tex]\textbf{B}[/tex] via [tex]\textbf{H} = - \nabla \Omega[/tex].

## The Attempt at a Solution

I'm desperately stuck on these; for both problems I can find [tex]\rho_m[/tex] and [tex]\sigma_m[/tex], but I don't see the connection to the [tex]\textbf{E}[/tex]-field. Any suggestions to get me started would be greatly appreciated.

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