PLEASE HELP! And Show work and explain :( (a) Three particles are arranged at th

Question

PLEASE HELP! And Show work and explain :(

(a) Three particles are arranged at the corners of an equilateral triangle. Two of the particles each have a charge of+20. 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 ofthe 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 +20. 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 +20. 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)   For three particles

     K*4Q = -2Kq - 2Kq

=>   q = - Q       ---------------> charge of third particle

b) For four particles

     K*4Q + K*4Q + K*4Q/sqrt2 = -2Kq - 2Kq -2Kq/sqrt2

=>   q = - 2Q       ---------------> charge of fourth particle

c)   For five particles

     K*4Q + K*4Q + K*4Q + K*4Q/1.618 + K*4Q/1.618 + K*4Q/1.618= -2Kq - 2Kq -2Kq/1.618 - 2Kq/1.618

=>   q = - 3Q       ---------------> charge of fifth particle

d) For ten particles

     By above pattern-

=>   q = - 8Q       ---------------> charge of tenth particle

e)   For two charges --------> it is in the middle of line joining the charges .

       For three charges --------> it is in the inside of triangle joining charges .

       For four charges --------> it is in the middle of square joining the charges .

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