# Potential difference due to attraction

#### gokul

The other day in my class, my professor said that:

'Whenever you have a force of attraction, the potential will always be negative'.
Why is that so?

#### ChipB

PHF Helper
Potential is a measure of the amount of work required to separate the two charges. Since the force of attraction at distance x is is F=K q_1 q_2/x^2, the energy required to separate them is:

U =int (K q_ q_2)/x^2 dx = -(K q_1 q_2)/x + C

where 'C' is the constant of integration. By convention 'C' is set to zero, which causes the potential to always be a negative number, and approach 0 as x goes to infinity. So potential is always negative for a system of two attractors - same thing applies to the potential energy of a mass in a gravitational field as well. The further apart you separate the two objects the less negative the potential becomes, until at x= infinity it's zero.

One advantage of selecting C=0 is that it makes the principal of conservation of mechanical energy quite simple:

W+U = 0.

#### gokul

Thanks a lot. This cleared it up.