Question

Find the magnitude of electric field (in $N/C$) due to a line charge of $\lambda =\left(2\sqrt{2}\right)nC/m$ at a point $P$ as shown

Answer 1

$\lambda =\left(2\sqrt{2}\right)nC/m$

Electric field at a point in front of a finite linear charged body is

$=\frac{k\lambda }{a}\left(\sin \alpha +\sin \beta \right)\left(\hat{j}\right)+\frac{k\lambda }{a}\left(\cos \alpha +\cos \beta \right)\left(\hat{i}\right)$

$E_p=\frac{9\times {10}^9\times 2\sqrt{2}}{12}\left(\frac{12}{15}-\frac{12}{20}\right)\left(\hat{i}\right)+\frac{9\times {10}^9\times 2\sqrt{2}}{12}\left(\frac{9}{15}-\frac{16}{20}\right)\left(\hat{j}\right)$

$E_p=\frac{9\times {10}^9\times 2\sqrt{2}\times 5}{12}\left(\hat{i}\right)+\frac{9\times {10}^9\times 2\sqrt{2}}{12}\times \frac{420}{15\times 20}$

$E_p=4.242\times {10}^8\left(\hat{i}\right)+29.694\times {10}^8\left(\hat{j}\right)$

${\left(E_p\right)}_{net}=29.995\times {10}^{8}N/C$