Imagine a large positive charge +Q fixed at some location in otherwise empty spa
ID: 2026372 • Letter: I
Question
Imagine a large positive charge +Q fixed at some location in otherwise empty space, far from all other charges. A positive test charge of smaller magnitude +q is launched directly towards the fixed charge. Of course, as the test charge gets closer, the repulsive force exerted on it by the fixed charge slows it down. Your job is to explain why the test charge slows down, but in terms of electric potential and EPE, rather than in terms of fields or forces.In particular:
explain how the electrical potential encountered by the test charge changes as it gets closer to the fixed charge, and why
explain how the EPE of the test charge changes as it gets closer to the fixed charge, and why
On that basis, explain why the test charge +q slows down as it approaches the fixed charge +Q.
Explanation / Answer
Electric potential is defined as kQ/r; it is inversely proportional to the distance from the charge.
When the charge is positive, the potential is positive everywhere and it gets larger (more positive) as you approach the charge.
Electric potential is an expression of the electric potential energy that a second charge would have if it were at that location. Electric potential energy is kQq/r; as you can see it is just the electric potential, multiplied by the second charge.
It is a basic law of physics that systems want to be at the lowest possible energy. Confronted with a potential energy gradient, they will tend towards the low value.
When you bring a positive charge in towards another positive charge, since the potential increases as you approach, so does the potential energy -- and as the potential energy increases, it takes away any kinetic energy that the incoming charge had, slowing it down.
Note that if the charges had different signs, then the potential energy would be negative and getting more negative as you approach; hence the charges would attract.