A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity)at the origin?

Question

Quizplus · Accepted Answer

The electric potential due to a uniformly charged linear segment is given by:
V = kλ∫dx/x
where k is the Coulomb constant, λ is the linear charge density, and the integral is taken over the segment.
Here, λ = Q/L = 4nC/2m = 2nC/m
So, V = 9x10^9 Nm^2/C^2 * 2nC/m * ln(6/x) from x=4m to x=6m
= 9x10^9 ln(3) V
= 1.13 V (approx)
Therefore, the correct integral for the electric potential at the origin is:
V = -9x10^9 Nm^2/C^2 * 2nC/m * ln(6)

A Charge of 4