- #1
timmastny
- 10
- 0
Homework Statement
Find the potential difference between V(P) - V(R) and V(c) - V(a)
Homework Equations
Electric potential:
V(a) - V(b) = [itex]\int^{b}_{a}[/itex]E*dr
V(b) - v(a) = -[itex]\int^{a}_{b}[/itex]E*dr
Fundamental Theorem of Calculus:
F(b) - F(a) = [itex]\int^{b}_{a}[/itex]f(x)dx
The Attempt at a Solution
My question is about the solutions attached. In the first example, we have V(P)-V(R), which makes the integral [itex]\int^{R}_{P}[/itex]E*dr. However, when evaluating the integral, the solution takes V(P)-V(R) which seems to disagree with the fundamental theorem of calculus. As per the bounds, I think it should be V(R)-V(P).
Note: while I think it is wrong, the online homework said that evaluting it V(R)-V(P) is incorrect.
Likewise, to add to the confusion, the second picture is the solution for V(c)-V(a), which makes an integral [itex]\int^{a}_{c}[/itex]E*dr. In this case, though, the solution is found by taking v(a)-v(c). (technically v(a) - v(b) because v(c)-v(b) is a constant). This result seems to follow the fundamental theorem of calculus and is the result I expected.
Finally, I thought maybe it had to do with the geometry so I attached a picture of the scenario. Hopefully some one can shed some light on the confusing integral bounds. Thanks