A point charge +q is located at x=1.0m. A second point charge -3q is located at

Question

A point charge +q is located at x=1.0m. A second point charge -3q is located at x=-1.0m.

1) Determine the rightward electric field for x<-1 in terms of q, x, and fundamental constants.
2) Determine the rightward electric field for -1< x <1 in terms of q, x, and fundamental constants.
3) Determine the rightward electric field for x>1 in terms of q, x, and fundamental constants.
4) What is the x-coordinate of the point at which the net electric field is equal to zero?
5) Graph the electric field E vs. postition X.

Please help by showing work.

Explanation / Answer

q @ x = 1.0
-3q @ x = - 1.0

1)
For x < -1
E = k*3q/(x+1)^2 - k*q/(x-1)^2

2)
For -1< x <1
E = k*3q/(x + 1)^2 + k*q/(1-x)^2

3)
For x > 1
E = - k*3q/(x+1)^2 + k*q/(x-1)^2

4)
For E Field to be Zero,
- k*3q/(x+1)^2 + k*q/(x-1)^2 = 0
3/(x+1)^2 = 1/(x-1)^2
x = 3.732 m

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