- #1
FS98
- 105
- 4
Homework Statement
A charge of 2 C is located at the origin. Two charges of −1 C each are located at the points (1, 1, 0) and (−1, 1, 0). If the potential φ is taken to be zero at infinity (as usual), then it is easy to see that φ is also zero at the point (0, 1, 0). It follows that somewhere on the y-axis beyond (0, 1, 0) the function φ (0, y, 0) must have a minimum or a maximum. At that point the electric field E must be zero. Why? Locate the point, at least approximately.
Homework Equations
φ = kq/r
The Attempt at a Solution
φ = 2k/y - 2k/sqrt(2-y)
The sqrt(2-y) comes from finding the distance between a given point on the y-axis and a particle through the Pythagorean theorom. The -2 coming from the fact that there are two negative charges with a magnitude of 1.
Then I took the derivative
dφ/dy = 2k(1/y^2-(1/2(2-y)^(3/2))
Set that equal to 0 and do some rearranging and crossing out.
y^2 = -2(2-y)^(3/2)
If I’ve done everything right up to this point, I don’t know how to solve for y in the final step.