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spaghetti3451
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Homework Statement
Determine the electric field and the charge density associated with the potential ##\displaystyle{V(r)=A\frac{\exp{-\lambda r}}{r}}##, where ##A## and ##\lambda## are constants.
Homework Equations
The Attempt at a Solution
The electric field is easy to determine:
##\displaystyle{{\bf{E}} = -\nabla V}##
##\displaystyle{= -A\ \nabla\left(\frac{\exp\left(-\lambda r\right)}{r}\right)}##
##\displaystyle{= -A\ \left(\frac{\partial}{\partial r}\left(\frac{\exp\left(-\lambda r\right)}{r}\right),0,0\right)}##
##\displaystyle{= A\ \left(\frac{(1+\lambda r)\exp\left(-\lambda r\right)}{r},0,0\right)}##
But the electric field is singular at the origin.
How does this affect the calculation of the charge density?