will rate thumbs up if you answer all parts Three charges are brought from infin

Question

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Three charges are brought from infinity and fixed at the vertices of a square of size 1m, as shown in the figure.

a) How much work is required to assemble the charges (include the sign)? +2nC 1nC +3nC b) What is the electric potential with respect to infinity at point P (include the sign)? c Can a direction be specified for the potential at point P? If so, draw an arrow at P to represent it. If not, why not? d) How much work would an external agent have to do to bring a fourth, negative charge of -2nC from infinity and place it at point P?

Explanation / Answer

(A) PE when very away, { PE = k q1 q2 / r }

PEi = 0

for this configuration,

PEf = [(9 x 10^9 x 2 x 10^-9 x -1 x 10^-9)/(1)] + [(9 x 10^9 x 3 x 10^-9 x -1 x 10^-9)/(1)] + [(9 x 10^9 x 3 x 10^-9 x 2 x 10^-9)/sqrt(1 + 1)]

PEf = - 6.82 x 10^-9 J

(B) V = k q / r

V = (9 x 10^9) [ (2 x 10^-9)/1 + (3 x 10^-9 / 1) + (-1 x 10^-9 / sqrt(2))]

V = 38.6 Volt

(C) potential is a scalar quantity.

so no direction.

(D) V = q deltaV  

V = (-2 x 10^-9)(38.6 - 0 )

V = - 77.3 x 10^-9 J

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