only annswer if you are sure please 2 a Twelve equal charge

only annswer if you are sure please :)

2. (a) Twelve equal charges, q, are situated at the corners of a regular 12-sided polygon (for instance, one on each numeral of aclock face). What is the net force on a test charge 0 at the center? (b) Suppose one of the 12 q\'s is removed (the one at \"6 o\'clock\"). What is the force on Q? Explain your reasoning carefully. (c) Now 13 equal charges, q, are placed at the corners of a regular 13-sided polygon. What is the force on a test charge Q at the center? (d) If one of the 13 q\'s is removed, what is the force on Q? Explain your reasoning.

Solution

a)The force on Q must be 0 by symmetry. The x, y, and z components of the fields due to each charge cancel, so the force vanishes.

b)Now it is like 10 of the charges cancel, the only one that doesn’t cancel being the one directly opposite the missing charge. Thus, the force is F = KQ*Q/R*R pointing in the direction of the missing charge. Here, r is the distance from the center to each charge.

c)Again, by symmetry, the answer is still 0.

d)The same answer as in part b, equation 1, and for the same reason.