A uniform electric field of magnitude 240 V/m is directed in the positive x direction. A...

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Physics

A uniform electric field of magnitude 240 V/m is directed in thepositive x direction. A +13.0 ÂµC charge moves from the origin tothe point (x, y) = (20.0 cm, 50.0 cm). (a) What is the change inthe potential energy of the charge field system? J (b) Through whatpotential difference does the charge move?

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Solution :-

a) The change in potential energy of the charge system isequal to workdone by the charge system

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Î”U = W = -qEd
Â Â Where
Â Â Â Â Â Â Â Â Â Â Â E = 240 i V/m
Â Â Â Â Â Â Â Â Â Â Â q = +13.0ÂµC
Â Â Â Â Â Â Â Â Â Â Â d = 0.20i + 0.50j

Â Â Â Â Therefore
Â Â Î”U = - (13Î¼C) * (240 i V/m)*(0.20i )
Â Â = - 6.24 x 10^-4 JÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â

b) The potential difference is
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Î”V = Î”U / q
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = - 6.9 x 10^-4 J / 15Î¼C
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = - 48 V

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