Answer to Question #293840 in Electricity and Magnetism for Wellen

Question

At the three consecutive corners of a square, 10 cm on each side, are point charges 4 x 10^-6 C, 8 x 10^-6 C, and 12 x 10^-6 C, respectively. Find the E_P at the fourth corner of the square.

Answer 1

$q_1=4\times10^{-6}C\\q_2=8\times10^{-6}C\\q_3=12\times10^{-6}C$

$a=10cm=0.1m$

Electric field due to $q_1$ Charge

$$E_1=\frac{kq_1}{r^2}=\frac{9\times10^{9}\times4\times10^{-6}}{0.1^2}=36\times10^{5}N/C$$

Electric field due to $q_2$ charge

$$E_2=\frac{kq_2}{r^2}=\frac{9\times10^{9}\times8\times10^{-6}}{(0.1\times\sqrt{2})^2}=36\times10^{5}N/C$$

Electric field due to $q_3$ ccharge

$$E_3=\frac{kq_3}{r^2}=\frac{9\times10^{9}\times12\times10^{-6}}{(0.1^2)}=108\times10^{5}N/C$$

Net electric field

$E'=\sqrt{E_1^2+E_3^2+2E_1E_3cos\theta}$

$$E'=\sqrt{36^2+108^2+2\times36\times108\times cos90°}=\sqrt{(36^2+108^2)\times10^{10}}$$

$$E'=\sqrt{1.296\times10^{14}}=113.48\times10^5N/C$$

Net electric field at point P

$E_{net}=E'+E_2$

$$E_{net}=36\times10^{5}+113.48\times10^{5}=149.48\times10^5N/C$$