10 Four charges are arranged on an xy grid Particle one has

10. Four charges are arranged on an x-y grid. Particle one has charge of +2e and sits at the origin. Particle two has a charge of 2e and sits at (0,2). Particle three has charge of 4e and sits at (2,0). Particle four has charge of -2e and is at a distance of 1.5m at an angle of 215\' from the positive x-axis. Find the magnitude and direction of the net electrostatic force on the particle located at the origin due to the presence of the other three.

Solution

X component of Force = 8.98*10⁹*4*1.6*10^-19*2*1.6*10^-19/4 + 8.98*10⁹*2*1.6*10^-19*2*1.6*10^-19*cos35/(2.615)²

                                                  = 45.977*10^-29 + 11.015*10^-29

                                       = 56.992*10^-29 N     ------------------> towards -x direction

Y component of Force = 8.98*10⁹*2*1.6*10^-19*2*1.6*10^-19/4 + 8.98*10⁹*2*1.6*10^-19*2*1.6*10^-19*sin35/(2.615)²

                                                  = 22.988*10^-29 + 7.713*10^-29

                                       = 30.701*10^-29 N    --------------------> towards -y direction

=> Net magnitude of electrostatic force = sqrt((56.992*10^-29)² + (30.701*10^-29)²)

                                       = 64.735*10^-29 N

Direction = 180 + tan-1(30.701/56.992)

                = 208.31 degrees from + x axis