Answer to Question #197483 in Electric Circuits for Ogunsakin Temidayo

Question

Three charges Q1= 2 microcoulomb (0,0)cm, Q2= 4 microcoulomb (0,10)cm and Q3= -3 microcoulomb (15,0)cm acts on one number another. Find the magnitude of the total electric force and the angle that the total electric force makes with the positive x-axis

Answer 1

$Q_1=2\times10^{-6}\space C$

$Q_2=4\times10^{-6}\space C$

$Q_3=-3\times10^{-6}\space C$

$F_{13}=k\dfrac{Q_1Q_3}{(15\times10^{-2})^2}=9\times10^9\dfrac{(2\times10^{-6})(3\times10^{-6})}{(15\times10^{-2})^2}$

$F_{13}=2.4\space N$

$F_{23}=k\dfrac{Q_2Q_3}{(18.02\times10^{-2})^2}=9\times10^9\dfrac{(4\times10^{-6})(3\times10^{-6})}{(18.02\times10^{-2})^2}$

$F_{23}=3.32\space N$

Angle between $F_{23}$ and $F_{13}$

$\tan\theta=\dfrac{10}{15}$

$\theta=33.69\degree$

Resultant force,

$F=\sqrt{F_{13}^2+F_{23}^2-2F_{13}F_{23}\cos\theta}$

$F=1.876\space N$

Angle made by resultant force with x axis

$\phi=180\degree-\dfrac{\theta}{2}=163.155\degree$