what might this HW question be asking?

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what might this HW question be asking?

Postby jjfortherear » Mon Sep 26, 2011 11:24 pm UTC

Asked to show that the mean-square charge radius of a uniformly charged sphere is <r^2>=(3/5)R^2. What exactly does this mean? Find the radius where Qenc = Qtot/sqrt(2)?

EDIT Well, obviously not 1/sqrt(2), since it isn't the rms, just mean square. So now no idea.
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Re: what might this HW question be asking?

Postby jmorgan3 » Mon Sep 26, 2011 11:58 pm UTC

What is the charge-averaged value of r^2 (i.e. x^2+y^2+z^2 for an origin-centered sphere) for the entire sphere?

EDIT: And how do you take averages over a continuous set?
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Re: what might this HW question be asking?

Postby Swivelguy » Fri Sep 30, 2011 2:53 pm UTC

I agree that the charge-averaged value of r2 sounds like what they're asking for. Because the charge is uniform, they might as well ask what the mean-square radius of a sphere is.

You solve this problem by taking a volume integral of r2 over a sphere and dividing by the volume of the sphere.
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