# Making sense of test charge motion when placing it in different places near a uniformly positive, nonconducting sheet

My question has to do with this graphic:

I am perfectly fine accepting the fact that the object will move parallel to $\vec E$ and perpendicular to the surface of the sheet. Any attraction from the upper parts of the sheet will be canceled out by the bottom or vice-versa. But, what if the test charge was raised up a bit, such that it was at the upper-half of the sheet when we begin to examine its motion?

Then, there "will be more things pulling it down" (for lack of a better word) than trying to pull it up (as there is more electric field lines below the particle than above it), so will it still move off perpendicular to the surface of the sheet or deflect downwards?

My guess is it will still move perpendicular, based off intuition and also due to the fact that, although there is less electric field lines above the test charge than below, due to the fact that the electrostatic force is an inverse square law, it'll still manage to cancel out.

Am I correct? And if not, why not?

• -1 Not clear what you are asking. Is the sheet infinite? If not, why are the field lines all perpendicular to the surface? If it is infinite, and the field lines are all perpendicular, why do you think the test charge will be "pulled down" parallel to the plane sheet? The test charge always starts to move in the direction of the local E field. – sammy gerbil Jan 30 '18 at 0:02
• Possible duplicate of Electric field of an infinite, uniformly charged layer with thickness $a$ – sammy gerbil Jan 30 '18 at 0:18