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!

 

[Nickie]

Can you help me out?

As a scientist, my response would be:

You have correctly set up the equation for the electric field at a point on the positive x-axis due to the three point charges. However, in order to solve for the point where the electric field is zero, you will need to use the principle of superposition and set the total electric field equal to zero. This means that the sum of the electric fields due to each individual charge must equal zero. You can then solve for x by rearranging the equation and using algebraic techniques. It may be helpful to plot the electric field as a function of x and visually determine where the electric field is zero.