In looking at the electric field about a pair of equal but opposite
fixed point charges situated on the x axis in my high school class, we
mapped part of the field by looking at the forces exerted on a test
charge (proton) by the two fixed charges. A student then asked me to
show that if one places the test charge to the left of the left-most
charge (the positive charge) but just slightly above the x axis that the
field line that it would follow would in fact 'circle' around in a large
path until it eventually approaches the other charge from the upper
right. It seems to me that the force of repulsion would always tend to
push the charge leftward making it difficult to see how it would ever
'circle' to the right.
Is there a way to see that the test proton will eventually move
rightward? Any help appreciated. Thanks.