Are there Electrostatic Fields at infinity?

AI Thread Summary
The discussion centers on the relationship between electrostatic potential and electric fields, particularly at infinity. The potential given is V(x) = x exp(-λx), and the question is whether there are electrostatic fields as x approaches infinity. It is suggested that there may be no fields at infinity due to the absence of electrostatic potential. The confusion arises from understanding how electric fields (E) relate to potential (V), with potential energy being defined in relation to charges. Clarification on this relationship is sought to resolve the confusion.
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Homework Statement


In the region x ≥ 0 there is an electrostatic potential V(x)=xexp(-λx) where λ>0
What is the electrostatic field at x→∞

Homework Equations





The Attempt at a Solution


My understanding is there is no fields at infinity because there is no electrostatic potential?
Sorry but I am so confused?
 
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How are the electric field E and the potential V related?
 
I believe Potential energy is the energy off one charge in relation to another charge. Therefore creating electrostatic fields? help:(
 

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