A uniform electric field of magnitude 257 V/mis directed in the negative x direc

Question

A uniform electric field of magnitude 257 V/mis directed in the negative x direction. A -15.1 uC chargemoves from the origin to the point (x, y) = (24.1cm, 48.7 cm). (a)What was the change in the potential energy of thischarge? (b) Through what potential difference did the chargemove?

EDIT
Nevermind, I got it. Thank you!



For (a) I did:
V =1/40 (-14.1e-6 C / r)
(0, 0) = (x1, y1)
(24.1 cm, 48.7 cm) = (x2, y2)
so r = (24.1 - 0)2 + (48.7 - 0)2
       = 54.3369 cm
       = .543369 m
given that constant 0 = 8.85e-12C2/Nm2
and U = qV where q = -14.1e-6 C, I got
V = 1/[4(8.85e-12 C2/Nm2)] * [(-14.1e-6 C/ .543369 m)
      = -2.3333e5 Volts
so plugging that into the U = qVequation, I got
U = (-14.1e-6 C)(-2.3333e5 V)
      = 3.28996
      = 3.29 J

But this is incorrect. Further I got the (b) part wrong and this iswhat I did:
(b) V = Er
         = (257V/m)(.543369 m)
         = 1.40e2 V

Can someone tell me how to fix what I did wrong? Thanks! Will ratelifesaver!

Explanation / Answer

change in potential energy = -q E x = .               = - -15.1 x 10-6 * -257 * 0.487 =   -0.001890 Joules . Note that since the E field is only in the x direction (not ydirection) only the x direction matters for the displacement. Thisis the same reason that since gravity only acts vertically, thepotential energy for an object is only affected by vertical motion(i.e. height) and not horizontal motion. . Anyway... now      U = q V .                   V = U / q = - 0.001890 / - 15.1 x 10-6=     125.1 Volts . Or...    V = - Ex = -   -257 * 0.487 =    125.1Volts . Note that since the E field is only in the x direction (not ydirection) only the x direction matters for the displacement. Thisis the same reason that since gravity only acts vertically, thepotential energy for an object is only affected by vertical motion(i.e. height) and not horizontal motion. . Anyway... now      U = q V .                   V = U / q = - 0.001890 / - 15.1 x 10-6=     125.1 Volts . Or...    V = - Ex = -   -257 * 0.487 =    125.1Volts

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