Asked to show that the meansquare 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.
what might this HW question be asking?
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what might this HW question be asking?
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Re: what might this HW question be asking?
What is the chargeaveraged value of r^2 (i.e. x^2+y^2+z^2 for an origincentered sphere) for the entire sphere?
EDIT: And how do you take averages over a continuous set?
EDIT: And how do you take averages over a continuous set?
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Last updated 6/29/108
Last updated 6/29/108
Re: what might this HW question be asking?
I agree that the chargeaveraged value of r^{2} sounds like what they're asking for. Because the charge is uniform, they might as well ask what the meansquare radius of a sphere is.
You solve this problem by taking a volume integral of r^{2} over a sphere and dividing by the volume of the sphere.
You solve this problem by taking a volume integral of r^{2} over a sphere and dividing by the volume of the sphere.
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