Question

Una barra de longitud de 2 m está cargada uniformemente y tiene una carga total de 5nC. Busqué su potencial eléctrico (relativo acero en el infinito) en un punto que se encuentra a lo largo del eje de la barra y está a 3m del centro de la barra?

Answer 1

Answer:

11.44J/C

Explanation:

To find the electric potential for a point at 3m from one extreme of the bar you use the formula for the electric potential:

$V=\int k\frac{dq}{r}=\int k\frac{dq}{x+3}$

Where r = x+3 represent the 3m distance of the charge to a point x in the bar.

dq: differential of charge = λdx. λ is the linear charge density.

k: Coulomb constant = 8.98*10^9 Nm^2/C^2

You can write dq as λdx. Furthermore, If you assume that the other extreme of the bar is at origin of the x-axis you can write the integral as follow:

$V=\int_{0}^{2}k\frac{\lambda dx}{x+3}\\\\V=k\lambda \ ln(x+3)|_{0}^{2}=k\lambda (0.510)$

You replace λ ad k in the last expression:

$V=(8.98*10^9Nm^2/C^2)(\frac{5*10^{-9}C}{2m})(0.510)=11.44\frac{J}{C}$

hence, the electric potential is 11.44J/C