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# what is electric potential due to an uniform infinitely charged electric sheet?

22 Points
4 years ago
Electric field is $\frac{\sigma }{2\epsilon }$ where sigma is the charge per unit area of sheet.

Va=$-\int_{\infty }^{r_{a}}E.dr=\frac{-\sigma }{2\epsilon }.(r_{a}-\infty )$

Vb=$-\int_{\infty }^{r_{b}}E.dr=\frac{-\sigma }{2\epsilon }.(r_{b}-\infty )$

$\Delta V = V_{b}-V_{a} = \frac{\sigma}{2\epsilon }.(r_{a}-r_{b})$
Thus the potential difference bwtween 2 pts due to the infinite sheet of charge is delta V as above