- #1

Z90E532

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## Homework Statement

Find the magnetic dipole moment of a spinning sphere of voltage ##V## and radius ##R## with angular frequency ##\omega##.

## Homework Equations

## The Attempt at a Solution

To find the dipole moment, we need to do ##I \int d \vec{a}##, which would be ##I 4 \pi R^2 \hat{r}##, but I need to find the current knowing only the voltage and angular velocity. I'm not sure how to proceed.

Edit: Thought about this again and noticed a mistake. What I need to do is integrate to add up all the current rings on the sphere. So I want to be able to do something like (the sphere is spinning along the z axis):

$$\vec{m} = \sigma R^3 \omega \int ^{2 \pi} _{0} \int ^{\pi} _{0} \sin^3 \theta d \theta \phi \hat{z}$$ .

Where ##I = \sigma R \omega \sin \theta## and ##\vec{A} = R^2 \sin^2 theta##

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