Question

Three point charges are arranged as shown in the figure. Calculate the magnitude and direction of the net electric force on the -3 nC charge.

https://imgur.com/a/bzKSbaz

Answer 1

force between point charges is

f = kq1q2/r^2

from the diagram

f21 = 9*10^9*5*10^-9*3*10^-9/(0.1)^2

f21 = 13.5*10^-6 j N

f31 = 9*10^9*6*10^-9*3*10^-9/r^2

r = sqrt(0.1^2+0.3^2) = 0.316 m

f31 = 9*10^9*6*10^-9*3*10^-9/(0.316)^2 = 1.62*10^-6 N

in vector form

f31 = 1.62*10^-6cos(45)i+1.62*10^-6sin45j

f31 = 1.145 *10^-6 i+1.145*10^-6 j N

f tot = f21+f31 = 1.145*10^-6 i+14.645*10^-6 j N

magnitude = 10^-6*sqrt(1.145^2+14.645^2) = 14.69*10^-6 N

direction = tan^-1(14.645/1.145) = 85.53 from x axis (or) 4.47 degrees from f21 force