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Question Number 37045 by ajfour last updated on 08/Jun/18

Commented by ajfour last updated on 08/Jun/18

$$Findelectricfieldatadistance$$$$r_{\mathrm{\perp }}fromalinechargeof$$$$uniformchargedensity,net$$$$chargeq.$$

Answered by ajfour last updated on 08/Jun/18

$$E=\int dE\cos \theta$$$$=\int \frac{\lambda dy\cos \theta }{4\pi {ϵ}_0{r}^2}$$$$r=r_{\mathrm{\perp }}\sec \theta$$$$y=r_{\mathrm{\perp }}\tan \theta \Rightarrow dy=r_{\mathrm{\perp }}\sec {}^2\theta d\theta$$$$E=\frac{q/l}{4\pi {ϵ}_0}{\int }_{-\alpha }^{\alpha }\frac{r_{\mathrm{\perp }}\sec {}^2\theta d\theta \cos \theta }{r_{\mathrm{\perp }}^2\sec {}^2\theta }$$$$=\frac{q/l}{4\pi {ϵ}_0{r}_{\mathrm{\perp }}}\left(2\sin \alpha \right)$$$$=\frac{q/l}{4\pi {ϵ}_0{r}_{\mathrm{\perp }}}\times \frac{2\times l/2}{r_{end}}$$$$E=\frac{q}{4\pi {ϵ}_0{r}_{\mathrm{\perp }}{r}_{end}}.$$

Commented by Tinkutara last updated on 08/Jun/18

Thank you very much Sir! I got the answer. ��������

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