# Is it possible create current by spinning a charged sphere?

If we have a sphere which has $σ$ surface charge density and rotate it in axis z will this create current ? Is it possible without any potential difference ?

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8.02 by any chance? – Janus Gowda Apr 26 '13 at 21:59

Yes. Let's assume that the charge density is fixed relative to the surface of a sphere of radius $R$, then spinning the sphere with angular velocity $\vec\omega = \omega \hat{z}$ would create a surface charge density $\vec K$ given by $$\vec K(\theta, \phi) = \omega R\sin\theta\sigma(\theta, \phi)\hat\phi(\theta, \phi)$$ where $\theta$ and $\phi$ are the polar and azimuthal spherical coordinates.
The total charge on the sphere is still just $\int \sigma dA$ even though the sphere is spinning; the motion does not change the amount of charge on the sphere. – joshphysics Apr 26 '13 at 21:54
By that do you mean the total charge per unit time passing through an arc on the sphere consisting of the portion of a great circle between $\theta = 0$ and $\theta = \pi$? If so, then yes, you would simply compute the integral $\int_0^\pi d\theta \,R \vec K\cdot\hat\phi$. – joshphysics Apr 26 '13 at 22:03