Point Where Electric Field=0 (3 point charges on x-axis)

[lola748]

Homework Statement

Point charges of -7 µC, 1.0 µC, and +7 µC are located along the x-axis at x = -1.0 cm, x = 0, and x = +1.0 cm, respectively. Locate a point on the positive x-axis where the magnitude of the electric field is zero.

Homework Equations

E=(kQ)/r^2
E(total)=E(1)+E(2)+E(3)

The Attempt at a Solution

I feel like I have the correct setup of the equation and just wanted to confirm:

E=0=-(7e-6/(x+1)^2)+(1e-6/(x^2))-(7e-6/(1-x)^2)

From this point I'm not really sure on how to proceed with solving for x.

 

[dfetnum]

You need to isolate the x, so you should multiply out the exponent and rearrange the problem in order to use the quadratic equation.

Edit: Actually don't isolate the x, just multiply the exponents out and group the similar exponents out.

Edit 2: Hmm, its not working for me, disregard post

 

[gneill]

Tip: When you're looking for zeros, you can discard all the common constants (same as setting your equation to zero and dividing both sides by the common constants). So your equation then looks like:

$$0 = \frac{-7}{(1 + x)^2} + \frac{1}{x^2} + \frac{-7}{(1 - x)^2}$$

Putting that over a common denominator and taking just the numerator yields a function that doesn't look promising for having positive real roots.

Edit: I take that back! I made a silly sign error on the last term (now fixed). There is a root betwixt 0 and 1.

 

[lola748]

Aaaaah I see, Thank you!