Calculate the force on charge 1 (find sum the total x and y forces.Given
α
=
6
0
,charge 1,2,3 have
+
1
1
×
1
0
−
6
coulombs of charge, and finally the distance between the charges is
.
1
5
m
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First we need our basic formulas F = d 2 K × q × q .Thus we have the equation lets calculate the force as follows F 2 1 = F 3 1 . 1 5 2 9 ∗ 1 0 9 × + 1 1 × 1 0 − 6 = 4 8 . 4 N . Now let us calculate the x , it is obvius that we are going to get F t o t a l x o f F 2 1 = f o r c e × c o s α = 4 8 . 4 ∗ c o s ( 6 0 ) = 2 4 . 2 and these the other f 2 1 =-24.2 so they cancel each other.Now we need the y forces acting in two directions first F t o t a l x i n 2 1 = f o r c e × c o s α = 4 8 . 4 ∗ s i n ( 6 0 ) = 4 1 . 9 and the the other y dirction F t o t a l x i n 3 1 = f o r c e × c o s α = 4 8 . 4 ∗ s i n ( 6 0 ) = 4 1 . 9 so the sum of those forces gives you 8 3 . 8 . Sorry explanation in picture would be more helpful but i don't know how to display picture
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Since the distance between each charge is the same, they must be on the vertices of an equilateral triangle. Therefore, the x-components of the electrostatic force cancel out, and the y-components of the forces from 2 and 3 will be the same (since they have the same charge).
Each y-component force will be F sin α where F = magnitude of the force. Hence:
Σ F = 2 sin α × r 2 k Q 1 Q 2 = 2 sin 6 0 o × 0 . 1 5 2 ( 8 . 9 9 × 1 0 9 ) ( 1 1 × 1 0 − 6 ) 2 = 8 3 . 7 N .