what is the difference between gravitaional potential energy and electrical potential energy of a charged partical

 

Lot of differences.

Nature, range & perhaps others.A detailed study might reveal contrasting differences and similarities.

 

Thats kind of like asking what the difference is between 100Watts of sound, and 100Watts of heat.. The 'potential' of the given energies would be the same (energy can be converted, but not created, nor destroyed), but the means by which that potential came to be would be different..
The only thing I disagree with Recca on is the range.. They both span to infinity as far as we know.. Charge exerts MUCH more force on charge at any given distance than matter exerts on matter gravititationally, but gravity is always attractive, while electrical energy is not, and charge has a tendency to arrange itself in relatively neutral clumps.. So electrical potential often works against itself (please overlook the horrendous wording of that statement), while gravity always acts constructively..

 

Firstly I assume that we are talking macro physics here. There is some debate about the nature and direction for forces at distances smaller than the size of an atom.

So for distances greater than this both laws are well defined and follow the same form.

However gravity applies to all particles, positive, negative or neutral whereas the electric field only affects positive and negative particles.
It does not impart Potential Energy to neutral ones, unlike gravity.

 

what is the difference between gravitaional potential energy and electrical potential energy of a charged partical

The graviational potential energy is due to the mass of the charged particle (masses develop forces between them)

The electrical potential energy is due to the charge of the particle (charged particles develop forces between them)

 

Another way of saying it is to look at their similarities as well. They are both potential energies. Potential energy is energy stored in an energy field. Think of it this way. If you let the particle go to where it wanted without restriction, it would enter a point of least energy. (I am assuming there are no troughs in the field here). The potential energy of a particle at point P is the amount of work that would need to be done to move the particle from the least energy location to P.

In the case of gravity potential, it is stored in a gravitational field.
The electrical potential is stored in an electrical field.

The magnitude of each is due to a property of the particle that has a value.
In the case of gravity, it is mass.
In electrical, it is charge.

They both have force being applied to them by the electrical field. This force is either the mass*gravitational field strength or charge*electrical field strength.

Note that one major difference arises because we do not know how to create negative masses. So all gravitational forces are attractive as opposed to electrical forces that can be both attractive and repulsive.