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A total amount of positive charge Q is spread onto a nonconducting, flat, circular annulus of inner radius a and outer radius b. The charge is distributed so that the charge density (charge per unit area) is giver by o = k/r^3, where r is the distance from the centre of the annulus to any point on it. Show that (with V = 0 at infinity) the potential at the centre of the annulus is given by:
V = (Q/8pie)((a+b)/ab)
so I have
dV = (1/4pie)(dQ/r)
dQ = odA = o2pirdr = 2piQdr/r^2
I'm really confused about the k in o = k/r^3
I'm thinking it must either be the constant k = 1/4pie, but my professor never rights that as k, so I'm thinking that k=Q because otherwise I don't see a way to have Q in the expression.
So I tried taking the integral of that expression from a to b with plugging dA and o in, but I'm not getting what I need.
Any help is much appreciated!
Thanks
V = (Q/8pie)((a+b)/ab)
so I have
dV = (1/4pie)(dQ/r)
dQ = odA = o2pirdr = 2piQdr/r^2
I'm really confused about the k in o = k/r^3
I'm thinking it must either be the constant k = 1/4pie, but my professor never rights that as k, so I'm thinking that k=Q because otherwise I don't see a way to have Q in the expression.
So I tried taking the integral of that expression from a to b with plugging dA and o in, but I'm not getting what I need.
Any help is much appreciated!
Thanks