# If I move a negative charge towards positive one on a rough surface then where does its potential energy go?

Suppose I have a positive charge and a negative charge at a distance on a rough table. The friction of the table overcomes the electrostatic force between them. So, they are stationary. Now, I push the negative charge a little more than the friction so that it moves towards the positive charge. In this process, I have given my energy to the negative charge in the form of its kinetic energy. Now, suppose that the charge stops midway to the positive charge due to constant opposition by the friction. In this process, all the kinetic energy has been converted into heat and the negative charge comes to rest, but at a new place. Now, the potential energy of the charge has decreased(since potential energy of a negative charge decreases with decrease in distance when it is attracted to a positive charge). So, my question is that where does this potential energy go? I just had given it MY energy and friction then converted it to heat. The electrostatic force was always less than the friction, and so it was always cancelled out. The remaining friction could have opposed MY force. So here did the potential energy vanish??

• Your potential energy, do u mean your gravitational potential energy? Commented Jul 10, 2020 at 5:53

First, note that this is not a question which is fundamentally electromagnetic in nature, so you could gain some intuition by imagining a block sliding down a rough inclined plane.

Imagine what the motion of the charge would have looked like in the absence of the electrostatic attraction from the positive charge. After you provided some kinetic energy in the form of the kick, the charge would move until that kinetic energy was surrendered to friction, at which point it would stop.

Now repeat the experiment in the presence of the positive charge. After your initial kick, the negative charge will lose energy to the friction, but gain energy from the electrostatic force. If the rate of energy loss is greater than the rate of energy gain, then the negative charge will eventually stop as before, but it will take longer; the friction has to absorb not just your initial kick, but also the additional work that the electric force does in the meantime.

Of course, if the energy gain exceeds (or is equal to) the energy loss, then the negative particle will never stop. This simply corresponds to the electric force being greater than the frictional force.

where does this potential energy go?

It went into heat - more than would have been generated in the absence of the positive charge.

• Everything went into friction. Reduced P.E of the charge ( due to force of attraction) and also the kinetic energy. Quick summary !!!
– user248823
Commented Jul 10, 2020 at 8:00