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## Homework Statement

Hi, here is the problem I'm having trouble with:

Three charges Q1, Q2, and Q3, each equal to 6.4 × 10–19 C, are in a straight line. The distance between neighboring charges is 60 nm. Find the magnitude of the electric field at P, which is 80 nm from Q2 on a line at right angles to the line between Q1 and Q3

## Homework Equations

E = kQ/r

^{2}

## The Attempt at a Solution

The correct answer is 1.9 x 10

^{6}N/C, but I cannot figure out how to arrive at that answer.

I started by first finding the magnitude of the electric field from each charge

E1 = kQ1/r

^{2}= (8.99 x 10

^{9}Nm

^{2}/C

^{2})(6.4 x 10

^{-19}C) / (100 x 10

^{-9}m)

^{2}= 575360 N/C

E2 = kQ2/r

^{2}= (8.99 x 10

^{9}Nm

^{2}/C

^{2})(6.4 x 10

^{-19}C) / (80 x 10

^{-9}m)

^{2}= 899000 N/C

E3 = kQ3/r

^{2}= (8.99 x 10

^{9}Nm

^{2}/C

^{2})(6.4 x 10

^{-19}C) / (100 x 10

^{-9}m)

^{2}= 575360 N/C

Then I tried splitting those into the x and y components

E

_{x}= 0, since E1

_{x}and E3

_{x}cancel each other out and there is no x component of E2

E1

_{y}= 575360sin[itex]\theta[/itex] = 345216 N/C

E3

_{y}would also equal this

E2

_{y}= 899000 N/C

E

_{y}= 1589432

so to find the magnitude of the resultant vector...

E = [itex]\sqrt{}[/itex](E

_{x}

^{2}+ E

_{y}

^{2})

E = [itex]\sqrt{}[/itex](0

^{2}+ 1589432

^{2}) = 1589432

E = 1.59 x 10

^{6}

So what am I doing wrong here? Any help would be appreciated