Electric Field of a Line of Charge

[Sarah Kumar]

If the electric field of a line charge at a distance 'a' is µ/2Π ε0a (µ is linear charge density), then the potential at that point should be µ/2Π ε0 (since potential = electric field x distance). This means that the potential is constant at every point around the line of charge. Hence, this means there is no potential difference between any two points around the line of charge. So, no work should be required to move a small charge from one point to another point around a line of charge. Is this conclusion correct?

 

[mfb]

(since potential = electric field x distance)

That formula only works for constant electric fields with zero potential at zero distance, but nowhere else.

By the way: Please put brackets around denominators, otherwise it is difficult to tell where the fraction ends.

 

[Dale]

the potential at that point should be µ/2Π ε0 (since potential = electric field x distance).

As @mfb correctly noted, this formula is incorrect. Here is a brief derivation of the correct formula:
https://www.miniphysics.com/uy1-electric-potential-of-an-infinite-line-charge.html