22nd September 2011 - 03:03 AM
Compute the potential difference between an initial point O(x=0,y=0) and P(x=9.00 cm,y=4.00 cm) if the electric field in the region is E = (8.50 N/C)(.300 ihat + .500 jhat).
distance between point O and point P = 0.09^2+0.04^2= 0.0097, sqrt = 0.0985m
magnitude of E is 8.5(.3) = 2.55 ihat, 8.5(.5) = 4.25 jhat
2.55^2 + 8.55^2 = 24.565, sqrt = 4.956 V/m
V=Ed------->0.0985m(4.956 V/m) = .488 V
which is wrong, is there a mistake?
22nd September 2011 - 03:27 PM
Hint: without calculating, what is the PD between the origin and any point along the line through the origin parallel to (0.5ihat-0.3jhat)? What does that suggest about your formula for V?
23rd September 2011 - 01:13 AM
am i right in assumig that you would take the dot product of the magnitude of the distance vector with the magnitude of the electric field?
23rd September 2011 - 05:02 AM
Since you're not the OP, answer in white below. Highlight to reveal.
Drop the 'magnitude's and you're spot on. Basically you need the magnitude of E times the magnitude of the distance parallel to the electric field. A bit of trig will show you that that is V=|E||x|cos(theta), where theta is the angle between the vectors. That is more compactly written V=E.x
23rd September 2011 - 06:39 AM
i dont mean to steal this persons thread, but out of my own intellectual curiousity--why is the value negative?
23rd September 2011 - 02:17 PM
It isn't. At least, I get a positive value. Post your working if you like - we'll see where we disagree.