Hi! I\'m really not sure how to answer this question, can anyone please help? Th

Question

Hi! I'm really not sure how to answer this question, can anyone please help? Thanks a ton!

(a) Three particles are arranged at the comers of an equilateral triangle. Two of the particles each have a charge of +2g. 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 ofthe particles each have a charge of +29. 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 +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 pattem from above! Ten particles are amanged 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 electrc field and the net electric potential equals zero.

Explanation / Answer

The sign of unknown charge will be positive as potential energy is given positive and known charge is positive and P.E. = Kq1q2/r.

And you can also say that potential given at origin also greater than the potential due to known charge hence unknown charge has to be positive.

Unknown charge must be placed on +ve x axis in order to get electric field in -ve x direction at origin as electric field lines are away from the positive charge.

Assume unknown charge is Q' and located at +x from origin.

P.E. = KQQ'/(x+d) = 2kQ2/d

Potential at origin KQ/d + KQ'/x = 4KQ/d

Solving both equations you will get x = 2d and Q' = 6Q.

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