- #1
richard7893
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Homework Statement
the electric potential of some configuration of charge is given by the expression:
V(r)= (Ae^(-pr))/(r)
where A and p are constants. Find the E-field E(r), the charge density rho(r) and total charge Q. The answer for rho is given in book as:
epsilon-not * A * ((1/r)4* pi* dirac delta^3 (r) - p^(2) e^(-p*r))
(The stuff inside parentheses is all divided by r
Homework Equations
-del V= E; del dot E = rho/epsilon-not ;
The Attempt at a Solution
I the took gradient of V using sperical coordinates using the formula
-del V= E
to obtain E.
Then I used the formula
del dot E = rho/epsilon-not
to find rho. I am not getting the same rho as in the book. I don't understand why the dirac delta function is in the answer. Do you have to perform an integration or am I taking a wrong apprach all together?