Question

Asked Apr 24, 2019

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A uniform line of charge with charge/length λ and length 2*l *lies along the x-axis extending from x= -*l* to x= +*l*. Determine the electric potential V(x) on the x-axis for x>1. Assume V=0 as x approaches infinity.

Step 1

The linear charge density of the line of charge is λ, the length of the line of charge is 2*l* centered at the origin.

Assumption: the potential at infinity is zero.

Step 2

Consider a small segment of the line charge *dx'* containing charge *dQ* at a distance *x'* from the point P. Here *x'* varies from *x−l* to *x+l* and also *x'>l*

The charge *dQ* is the product of the linear charge density and the thickness of the segment which is λ*dx'*.

Write the potential due to this segment of charge.

Step 3

Integrate the above equation in the limit *x−l* to *x+l...*

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