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coffeem
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Homework Statement
a) What is the value of an electrostatic potential V, a distance r from a point charge Q?
b) A uniform line of charge, of linear charge density ([tex]\lambda[/tex]), extends along the x-axis from x = 0, to x = a.
i) By considering the contributions from the infitisimal elements of the charge, show that the electrostatic potential at a point on the x-axis with x = b, where b>a, is given by:
V(b) = [tex]\stackrel{\lambda}{4pie0}[/tex]ln([tex]\frac{b}{(b-a)}[/tex]
ii) Explain how the electrical field E can be derived from the distribution of the electrostatic potential.
iii) By considering how the potential varies with b, find the electrostatic field along the x-axis, again for b>a.
iv) Demonstrate that the value for E you have determined is consistant with that expected from an equivalent point charge, in the limit b>>a.
The Attempt at a Solution
a) for this is simply have: v =Q/4pie0r.
b) I know that I am dealing with a continuous charge distribution problem here. But have no idea how I can show that... any advice would be appreciated. Thanks