Relatively hard. Won't you say?

Calculate the force on charge 1 (find sum the total x and y forces.Given α = 60 \alpha =60 ,charge 1,2,3 have + 11 × 1 0 6 +11\times 10^ -6 coulombs of charge, and finally the distance between the charges is . 15 m .15m


The answer is 83.8.

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2 solutions

A K
May 5, 2014

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 F\sin \alpha where F F = magnitude of the force. Hence:

Σ F = 2 sin α × k Q 1 Q 2 r 2 = 2 sin 6 0 o × ( 8.99 × 1 0 9 ) ( 11 × 1 0 6 ) 2 0.1 5 2 = 83.7 N {\Sigma} F = 2\sin\alpha\times \frac{kQ_{1}Q_{2}}{r^2} = 2\sin 60^{o} \times \frac{(8.99{\times}10^{9})(11{\times}10^{-6})^{2}}{0.15^{2}} = \boxed{83.7N} .

First we need our basic formulas F = K × q × q d 2 F=\frac { K\times q\times q }{ d^ 2 } .Thus we have the equation lets calculate the force as follows F 21 = F 31 9 1 0 9 × + 11 × 1 0 6 . 1 5 2 = 48.4 N { F }_{ 21 }={ F }_{ 31 }\frac { 9*10^ 9\times +11\times 10^{ - }6 }{ .15^ 2 } =48.4N . 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 21 = f o r c e × c o s α = 48.4 c o s ( 60 ) = 24.2 { F }_{ total x of F 21 }=force\times cos\alpha =48.4*cos(60)=24.2 and these the other f 21 f 21 =-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 21 = f o r c e × c o s α = 48.4 s i n ( 60 ) = 41.9 { F }_{ total\quad x\quad in\quad 21 }=force\times cos\alpha =48.4*sin(60)=41.9 and the the other y dirction F t o t a l x i n 31 = f o r c e × c o s α = 48.4 s i n ( 60 ) = 41.9 { F }_{ total\quad x\quad in\quad 31 }=force\times cos\alpha =48.4*sin(60)=41.9 so the sum of those forces gives you 83.8 \boxed{83.8} . Sorry explanation in picture would be more helpful but i don't know how to display picture

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