Potential Energy vs. Electrical Potential

# Potential Energy vs. Electrical Potential - q at centers of...

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Charges -2 q at corners of equilateral triangle, + q at centers of sides. Side length 2 d . What’s U ? –2 q + q d 6 charges Î 5+4+3+2+1=15 pairs 3 d 3 – to – pairs: U = k (-2 q )(-2 q )/(2 d )= 2 kq 2 / d 3 + to + pairs: U = k ( q )( q )/( d )= kq 2 / d 6 – to + pairs: U = k (–2 q )( q )/( d )= –2 kq 2 / d 3 – to + pairs: U = k (–2 q )( q )/( 3 d )= –(2/ 3) kq 2 / d U = (6 +3 –12 –6/ 3) kq 2 / d = –(3 +2 3) kq 2 / d

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Charges -2 q at 2 corners of equilateral triangle,
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Unformatted text preview: + q at centers of sides. Side length 2 d . What’s V at 3 rd apex? –2 q + q d 3 d For V calculation, ignore pre-existing pairs. 5 terms needed. 2 – charges: V = k (–2 q )/(2 d ) = – kq / d 2 + close: V = k ( q )/( d ) = kq / d 1 + far: V = k ( q )/( √ 3 d ) = (1/ √ 3) kq / d V = (1/ √ 3) kq / d (others cancel)...
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Potential Energy vs. Electrical Potential - q at centers of...

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