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## Homework Statement

Figure 22-7a shows three particles with charges q1= +2Q,

q2=-2Q, and q3 = -4Q, each a distance d from the origin.

What net electric field E is produced at the origin?

## Homework Equations

E=q/r^2* 1/(4∏ε0)

## The Attempt at a Solution

So i calculated the of each particles separately.

E1= (2Q/d^2)*1/(4∏ε0)

E2= (-2Q/d^2)*1/(4∏ε0)

E3=(-4Q/d^2*1)/(4∏ε0)

now ƩFx= [-E1cos(30)-E2cos(30) -E3cons(30)]1/(4∏ε0)

ƩFx= (-8Q/d^2)*cos(30)*1/(4∏ε0)

ƩFy= [E1sin(30)+E2sin(30)-E3sin(30)]1/(4∏ε0)

ƩFy= 2Q/d^2*sin(30)+2Q/d^2*sin(30) -4Qsin*(30)

ƩFy=0

this means that we have a net electric field on the negative x direction of -8Q/d^2 *cos(30)*(1/(4∏ε0)).

however, my book has the same answer but in the positive x direction. they used a different method to solved this.

I attached the book's answer.

what did i do wrong?