Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What is the electric potential (relative to zero at infinity) at the origin (x = 0)?
A) 91 V
B) 99 V
C) 82 V
D) 74 V
E) 140 V

Question

Quizplus · Accepted Answer

The electric potential $V$ due to a line charge at a point is given by the formula $V = \frac{\lambda}{4\pi\epsilon_0} \ln\left(\frac{r_2}{r_1}\right)$, where $\lambda$ is the linear charge density, $\epsilon_0$ is the permittivity of free space ($8.85 \times 10^{-12} \, \text{C}^2/\text{N}\cdot\text{m}^2$), $r_1$ and $r_2$ are the distances from the point to the ends of the line charge. Given $\lambda = 12 \, \text{nC/m} = 12 \times 10^{-9} \, \text{C/m}$, $r_1 = 2 \, \text{m}$, and $r_2 = 5 \, \text{m}$, substituting these values gives $V = \frac{12 \times 10^{-9}}{4\pi \times 8.85 \times 10^{-12}} \ln\left(\frac{5}{2}\right)$, which calculates to approximately 99 V.

Charge of Uniform Density 12 NC/m Is Distributed Along the X