How Does Electric Field Affect Potential Change Between Two Points?

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To determine the change in electric potential between two points A and B in a uniform electric field E=5i+4j V/m, one must calculate the potential difference using the formula ΔV = -∫E·dr. The coordinates for point A are given as (-1m, -1m) and for point B as (1m, 2m). The discussion highlights uncertainty about whether to calculate the difference directly or apply trigonometric methods. Clarification on the appropriate method for this calculation is sought. Understanding the relationship between electric fields and potential changes is crucial for solving such problems.
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I would be very grateful if you could help point me in the right direction. Thanks[


b]1. Homework Statement [/b]
If a uniform field E=5i+4j V/m what would be the change in potential from A(-1m, -1m) to B at (1m,2m).
Thanks.



Homework Equations





The Attempt at a Solution


Not sure whether to do the difference between them, or use some trig.
 
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Difference.
 
(a) The polarisation pattern is elliptical with maximum (1,1) and minimum (-1,-1), and anticlockwise in direction. (b) I know the solution is a quarter-wave plate oriented π/4, and half-wave plate at π/16, but don't understand how to reach there. I've obtained the polarisation vector (cos π/8, isin π/8) so far. I can't find much online guidance or textbook material working through this topic, so I'd appreciate any help I can get. Also, if anyone could let me know where I can get more...

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