If we want to push an electron towards another electron we give equal but opposite force which means we push the electron with the same amount of force that it is being pushed back. Shouldn't both the forces cancel out the electron remain stationary?
If you give an equal force to the electron the forces will be neutral so a force greater than the neutral state shall be needed to push
The forces are on two different particles they would only cancel if the two forces acted on the same object in equal magnitude and opposite direction.
No. We're applying a force to electron that is greater than the repulsive force, so the forces on the electron are not balanced and it moves. The "equal and opposite force" is the force the electron exerts on us when we're pushing on it.
"F in the definition of potential energy is the force exerted by the force field, e.g., gravity, spring force, etc. The potential energy U is equal to the work you must do against that force to move an object from the U=0 reference point to the position r. The force you must exert to move it must be equal but oppositely directed, and that is the source of the negative sign. The force exerted by the force field always tends toward lower energy and will act to reduce the potential energy." - Hyperphysics The above definition tells us that equal and opposite force must be exerted to move an object against a field. How can the object move?
This is not true in general. If you have an equal and opposite force then there will be no acceleration, but that is not required in general. Also, equal and opposite forces on a single object imply no acceleration, not no movement. It will continue moving with it's initial velocity.
No, you are misunderstanding the issue. The issue is that all forces - all forces come in equal and opposite pairs. When you push on a box on the floor and it doesn't move due to friction, that isn't two forces, that's four. Two pair: -You push on the box and it pushes back. -The box pushes on the floor and the floor pushes back. See, Newton's 3rd law is talking about force pairs, whereas Newton's second law is talking only about the force applied to the body, not the reaction force applied back.
Yes, specifically the statement that I quoted is wrong and is the one that is the source of your confusion.
Agreed - but the OP is. He just doesn't know it. "Not true in general" isn't the same as "wrong". I agree that it isn't true in general, but I disagree that it is wrong. What it is is simplified for the sake of explanation. We often get the question here that if potential energy (gravitational, for example) is equal to the force of gravity times distance, how can the object move? The answer is a limiting case of a force negligibly above the weight. For introductory or practical purposes I don't see it as being important to go into that when one first explains it. If someone asks, fine, but if not, it saves a little time. In either case, regardless of the force applied, the force that contributes to the potential energy is exactly equal to the weight. But none of that has anything to do with the original question. The original question was if you push on something and it pushes back with an equal and opposite force, how can it move? That's confusing Newton's 2nd and 3rd laws.
I think it's clear from the context that the question is not about Newton's 3rd law. You push an electron towards another with exactly an equal an opposite force that the other electron is exerting. All forces in question act on the electron. The question doesn't talk about anything pushing back on you.
The point that the OP raises is a subtle point often glossed over in texts, as it is in the Hyperphysics statement quoted. In order to change the position of a charge q at rest in an electric field, E, it is not enough to give it a force equal to -qE. That just keeps it in the same position. One has to apply a force to that charge that is greater in magnitude than |-qE|. The application of this force gives q some kinetic energy. A change in potential energy comes from a loss of that kinetic energy when the charge returns to rest in a new position. AM
Your point is well taken. However, the OP is dealing with a situation in which a charge is held at a certain position in an electric field. This means that a force of -qE has to be applied to the charge in order to keep it there. The force required to move that charge (to change its position) must be greater than -qE. I have edited my post to make that clear. AM