The line element dx is intercepted on the table, and the coordinate is x, and the potential to point O is dU=kdqa/(2L+x) = -kaλdx/ (2L+x), (x < 0).

So the potential in the left half is u-= ∫-l to 0 (-k? aλdx/ (2L+x)？ )=kaλln ( 1/2).

Potential contribution of the right half:

Cut off the line element dx on the table, the coordinate is X, and its potential to point O is dU=kdqa/ (2L+x) = k? aλdx/ (2L+x)，(x & gt0)。

So the potential in the right half is u+= ∫-l to 0 (k? aλdx/ (2L+x)？ )=kaλln (3/2).

Total u = (u-)+(u+) = ka λ ln (1/2)? +? kaλln (3/2) =kaλln(3/4).

Extended data:

From the macroscopic effect, the charge on the charged body can be considered as continuous distribution. The density of charge distribution can be measured by charge density. The charge of volume distribution is measured by charge volume density, and the charge of area distribution and line distribution is measured by charge surface density and charge line density respectively. A measure of charge distribution density.

Assume that the charge is distributed in a curve or a straight bar, and its linear charge density is the charge per unit length, and the unit is coulomb/meter. Assume that the charge is distributed on the surface of a plane or an object, and its surface charge density is the charge per unit area, and the unit is coulomb/square meter.

Assume that the charge is distributed in a certain area or object in three-dimensional space, and its bulk charge density is the charge per unit volume, in coulomb/cubic meter.