# A uniform line of charge with charge/length λ and length 2l 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.

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A uniform line of charge with charge/length λ and length 2lies 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.

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Step 1

The linear charge density of the line of charge is λ, the length of the line of charge is 2l 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  λdx'.

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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