(a) Three particles are arranged at the corners of an equilateral triangle. Two
ID: 2002419 • Letter: #
Question
(a) Three particles are arranged at the corners of an equilateral triangle. Two of the particles each have a charge of +2Q. The net electric potential energy of the three particles is zero. What is the charge of the third particle?
(b) Four particles are arranged at the corners of a square. Three of the particles each have a charge of +2Q. The net electric potential energy of the four particles is zero. What is the charge of the fourth particle?
(c) Five particles are arranged at the points of a five-pointed star (or, equivalently, at the vertices of a pentagon). Four of the particles each have a charge of +2Q. The net electric potential energy of the five particles is zero. What is the charge of the fifth particle?
(d) Hint: build on the pattern from above! Ten particles are arranged at the vertices of a regular 10-sided figure. Nine of the particles each have a charge of +2Q. The net electric potential energy of the ten particles is zero. What is the charge of the tenth particle?
(e) Sketch a configuration of two or more charges in which there is a point (clearly identify the point) where both the net electric field and the net electric potential equals zero.
Explanation / Answer
a)
F = (k/r^2)*( Q^2+2qQ) = 0
q = -Q/2
b)
PE = k ( 4Q^2/L+4Q^2/L+2Qq/Sqrt(2L)+4Q^2/Sqrt(2L)+2Qq/L+2Qq/L) =0
8Q^2/L+4Qq/L+2Qq/Sqrt(2L)+4Q^2/Sqrt(2L) =0
8Q/L+4q/L+2q/Sqrt(2L) +4Q/Sqrt(2L) =0
q = - ( 4Q/Sqrt(2L)+8Q/L)/(4/L+2/Sqrt(2L)
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