Finding the electric field along the line between charges

Aug 2019
So I've been asked this question as part of my physics assignment (Its an advanced section question so significantly harder than the normal questions) and I've been stuck, my intuition tells me there should be two zero points, and initially I found a formula that only found one, however retrying the question with the new working attached here finds two zero points except the formulas feel wrong. Note, I haven't found the zero points analytically in the working, I've instead been graphing the formula each time to see how it appears (I've also attached the two functions graphed)

The question is as follows:

Derive an expression for the electric field along the vertical line that passes through the negative charge. How many times does the electric field strength pass through zero? For each such zero-point of the field, what would happen if a positive test charge was released from rest near to(but not directly on top of) the point where the field is zero?

The diagram is attached as a jpg as to how the charge set up looks
Any help would be great



Forum Staff
Apr 2008
On the dance floor, baby!
Hint: The electric field due to either of the \+- charges act along the line connecting them. So you would have the vector sum E(tot) = E_{c1} + E_{c2}[/tex] where c1 is the + charge on the left and c2 is the + charge on the right. See where this leads to.

You could also solve this by using the total potential at point d, but I'm going to guess you aren't there yet.