Potential difference between two points located at distances

[jeff1evesque]

Homework Statement
Find the potential difference between two points located at distances $$R_1$$, and $$R_2$$ from a point source.

Solution
Potential difference = $$V_{p_1, p_2} = V_{abs_1} - V_{abs_2}$$.

Question
Hows is the solution above true? What if the angle formed between $$P_1, Q, P_2$$ increases? Don't we have to take this into consideration? If the angle increases, then $$P_1$$ will be at a larger distance away from $$P_2$$ (at least until an angle of $$\pi$$). Doesn't distance influence the potential difference?

Thanks again,

JL

 

[rl.bhat]

Potential difference depends on the position of P1 and P2 with respect the the field, not on the path from P1 to P2.

 

[jeff1evesque]

Potential difference depends on the position of P1 and P2 with respect the the field, not on the path from P1 to P2.

Is that a definition, or can it be justified?

 

[rl.bhat]

Yes. It is the basic theorem.
If you lift an object to certain height, rise in potential energy is = mgh, irrespective of the path through the object is taken.

 

[merryjman]

Both electric fields and gravity fields, which rl.bhat mentions, are called conservative fields, meaning that the path taken from A to B does not matter. Friction is non-conservative, by counterexample. Since the electric field is conservative, you can describe its potential with a scalar rather than a vector. You're right that distance affects potential difference sometimes, but this is taken into account when you calculate the individual potentials V1 and V2. But because it's a scalar potential, the angle does not matter, only the distance.