What is the difference between a point charge [math] q [/math] and a test charge [math] q_0 [/math] ?

 

When dealing with electric potential, my book gives one equation when dealing with a test charge:

 

[math] V = EPE/q_0 [/math]

 

and one when dealing with a point charge:

 

[math] V = kq/r [/math]

 

Why is there a difference between the two?

I´ve no idea, mainly because I am unsure what "EPE" is. I do know the term "test charge" as a negligibly small charge that´s put into an electric (or even electromagnetic) field to measure it by observing the reaction of the test charge due to the influence of the electric field; for example by determining the force F=qE acting on it. So in your case I´d assume the potential is reconstructed from the information obtained by some test charge (as opposed to the other case, where the point charge q is the source of the field). Just a guess, though (please state what "EPE" is, I´m probably not the only one who doesn´t see that).

EPE is just the electric potential energy. But I think I get what you're saying, the difference is a point charge creates and electric field, and a test charge, with negligible charge is placed into an electric field to measure the electric force that acts on the test charge itself, right?

EPE is just the electric potential energy. But I think I get what you're saying, the difference is a point charge creates and electric field, and a test charge, with negligible charge is placed into an electric field to measure the electric force that acts on the test charge itself, right?

 

Right. The test charge can be used to map out any field from any configuration, e.g. the ~constant field inside the plates of a capacitor. The point charge is one specific configuration, though you can use superposition to construct any situation from a collection of point charges.

Alright I get it, thank you both

EPE is just the electric potential energy.

Ok, so just to add: In this case you can see the 1st equation as the definition of what the electic potential is supposed to be: The potential energy a test charge would have normalized to the test charge's electric charge. The 2nd equation tells you how to actually calculate this potential from a given charge distribution (potentials from different charges just add up, so you can calculate the potential for arbitrary charge distributions, as Swansont mentioned).