Given the arrangement of charged particles in the figure bel

Given the arrangement of charged particles in the figure below, find the net electrostatic force on the q_1 = 5.75 meuC charged particle. ( Assume q_2 = 11.33 meu C and q_3 = -22.12 meu C. Express your answer in vector form.)

Solution

For the charge particles with charges q1 and q2 and separated by a distance r, net force acting between them is given as F = Kq1*q2/r^2

Now as for the given situation, we would determine the forces acting along the x and y axis independently and for that we would need the distance between the particles and the angle made by the line joining them with the x axis.

Distance between, Q1 and Q2 = sqrt(1 + 9) = sqrt10 cms

Distance between Q1 and Q3 = sqrt(4 + 1) = sqrt5 cms

Further, it needs to be understood that the unlike charges attract each other while like charges repel.

Now, the net force acting along the x axis would be sum of x components of the individual forces acting on the particle.

Fx = Kq1 [Q3* 2 / 5 * (sqrt5) x 10^-4 - Q2* 3 / 10* sqrt10 x 10^-4]

Fx = 8.99 x 10^9 x 5.75 x 10^-8 [22.12 x 2/ 5 * sqrt5 - 11.33 x 3 / 10*sqrt10]

Fx = 8.99 x 10 x 5.75 (3.957 - 1.0749) = 1.4898295 x 10^3 N

Now, Fy = Kq1[- Q3 * 1 / 5 * sqrt5 x 10^-4 - Q2* 1 / 10*sqrt10*10^-4]

Fy = 8.99 x 10^9 x 5.75 x 10^-8 [- 22.12 / 5 * sqrt5 - 11.33 / 10*sqrt10]

Fy = -1.20794 x 10^3 N

Therfore, the net force acting on Q1 is given as: 1.4898295 x 10^3 i -1.20794 x 10^3 j N