Question

# Three charges are arranged as shown in Figure. Find the magnitude and direction of the electrostatic force on the charge at the origin.

Other
Three charges are arranged as shown in Figure. Find the magnitude and direction of the electrostatic force on the charge at the origin.

2021-03-25
Force between two charges on x-axis is repulsion force, so the force on charge at origin acts in negative x-direction
$$\displaystyle{F}_{{1}}={k}{\left({6}\cdot{10}^{{-{9}}}\right)}{\frac{{{5}\cdot{10}^{{-{9}}}}}{{{\left({0.03}\right)}^{{2}}}}}={8.98}\cdot{10}^{{{9}}}\cdot{\left({6}\cdot{10}^{{-{9}}}\right)}{\frac{{{5}\cdot{10}^{{-{9}}}}}{{{\left({0.03}\right)}^{{2}}}}}$$
$$\displaystyle={2993.33}\cdot{10}^{{-{9}}}$$ N
Force between two charges on y-axis is attractive force, so the force on charge at origin acts in negative y-direction
$$\displaystyle{F}_{{2}}={k}{\left({3}\cdot{10}^{{-{9}}}\right)}{\frac{{{5}\cdot{10}^{{-{9}}}}}{{{\left({0.01}\right)}^{{2}}}}}={8.98}\cdot{10}^{{{9}}}\cdot{\left({3}\cdot{10}^{{-{9}}}\right)}{\frac{{{5}\cdot{10}^{{-{9}}}}}{{{\left({0.01}\right)}^{{2}}}}}$$
angle made by the net force with positive x-axis = 180 + taninverse $$\displaystyle{\frac{{{13470}\cdot{10}^{{-{9}}}}}{{{2993.33}\cdot{10}^{{-{9}}}}}}={180}+{77.47}={257.77}$$ degrees
magnitude of force $$\displaystyle=\sqrt{{{13470}^{{2}}+{2993.33}^{{2}}}}\cdot{10}^{{-{9}}}={13798.5}\cdot{10}^{{-{9}}}$$ N