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NiendorfPhysics
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Homework Statement
The Spherical region a<r<b carries a charge per unit volume of $$\frac{A}{r}$$, where A is constant. At the center there is a point charge q. Find A such that the Electric field in a<r<b is constant.
Homework Equations
Law of superposition and $$E=\frac{kq}{r^2}$$
The Attempt at a Solution
$$E=k(\frac{q}{r^2}+\frac{\frac{A}{r}*\frac{4\pi(r^3-a^3)}{3}}{r^2})$$
$$\frac{dE}{dr}=0=\frac{-2q}{r^3}+0+\frac{4A{\pi}a^3}{r^4}$$
$$A=\frac{qr}{2{\pi}a^3}$$
Which means that I got that no constant would satisfy the stated condition. Answer in the back is $$A=\frac{q}{2{\pi}a^2}$$. Any hints are appreciated.
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