Uniform electric field?

Question

A uniform electric field of magnitude 292 V/m is directed in the positive x direction. Suppose a 21 microC charge moves from the origin to point A at the coordinates (.27m, .60m). What is the absolute value of the change in potential from the origin to point A? Answer in V.

Answer 1

change in potential energy = work done in moving charge at an angle to the force direction (x-axis)

Here charge would like follow the x-axis, but being taken in x-y plane (obliquely)

Force on charge F = Q E= 292* 21 *10^-6 N (along x-axis)
Vector form Fv = 292 (i)
Displacement d = meter in x-y plane
from (0,0) to (0.27m, 0.60m)
vector form dv = 0.27 (i) + 0.60 (j)

Angle between F and d = cos (thita) = 0.27 / d

Change in PE = F d cos(thita) = (292* 21 *10^-6) (d ) 0.27/d
= (292* 21 *10^-6) 0.27
= (292* Q) 0.27
----------------------
vector form: Delta PE = (Fv) DOT (dv)
= [292 (i)] . [0.27 (i) + 0.60 (j)]
= 292 Q* 0.27 just as -----(1)
-----------------

Change in absolute potential = change in P. energy/charge
= (292*Q) 0.27/Q = 78.84 volts

Answer 2

potential difference= - 292x.27 V