Question

Four charged particles are at the corners of a square of side a, as shown in the figure below. (A = 4, B = 5, C = 5.)

(a) Determine the magnitude and direction of the electric field at the location of charge q. (Use k_e for the Coulomb constant and q and a as necessary.)
Magnitude
______
Direction
______° (counterclockwise from the horizontal)

(b) What is the total electric force exerted on q?
Magnitude
_____
Direction
_____°(counterclockwise from the horizontal)

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I've figured this much:

[(k_e*4q)/(a^2)]i-hat + [(k_e*5q)/(2a^2)](i-hat cos 45 + j-hat sin 45) + (k_e*5q)/(a^2)]j-hat

----> ?

But I don't know how to simplify it from there, though I know my final answer needs to be:
_____*k_e*q)/(a^2)

Answer 1

Oh picture looks like this

4q----a----q
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a a
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5q----a----5q