We study three point charges at the corners of a triangle as

We study three point charges at the corners of a triangle, as shown in the figure below. Their charges are q1 = +3.0 x 10-9 C·92 =-3.5 x 10-9 C, and q,-+4.0 x 10-9 C·Two distances of separation are also given, 112 2 m and 113-3 m. Find the net electric force (in N) on q3 42 43 12 13 41 Fnet, x 5.0e-09 = Fnet, y = 8e-09 Need Help? Read

Solution

First determine the distance l23 -

l23 = sqrt[l13^2 - l12^2] = sqrt[3^3 - 2^2] = 2.24 m

Force due to charge q1 on q3 -

F13 = k*q1*q3 / l13^2 = (9x10^9x3x10^-9x4x10^-9) / 3^2 = 12 x 10^-9 N

Resolve its component in x and y directions -

F13x = F13*cos45 = 12x10^-9xcos45 = 8.48 x 10^-9 N

F13y = F13*sin45 = 12x10^-9xsin45 = 8.48 x 10^-9 N

Force due to charge q2 on q3 -

F23 = k*q2*q3 / l23^2 = (9x10^9x-3.5x10^-9x4x10^-9) / 2.24^2 = -25.11 x 10^-9 N

So, net force in the x - direction,

Fnet,x = -25.11 x 10^-9 + 8.48 x 10^-9 = -16.63 x 10^-9 N

Net force in the y - direction -

Fnet,y = 8.48 x 10^-9 N