the question is:
Without doing any calculations, explain why the divergence of each of the functions must be zero(Hint: consider what electric field these functions physically correspond to)
P.S: I make the unit vectors in bold.
A2=ρ(1/ρ) with ρ>0
A3=r(1/r2) with r>0
I think we need to argue about the charge
The Attempt at a Solution
for A1 , the electric field of A! is a plane, which constant, so divergence is zero.
for A2, it seems to be a line of charge but I don know how to argue for the divergence to be zero.
Same for A3
Can someone see what is going on?