Four charges ( q 1 = + Q , q 2 = +2 Q , q 3 = ? 3 Q , and q 4 = +2 Q ,) are arra

Question

Four charges (q1 = +Q, q2 = +2Q, q3 = ?3Q, and q4 = +2Q,) are arranged as in the figure in the corners of a square with sides of length d.

(a) Find the total electric potential energy stored in this system (relative to U = 0 when they are at infinitely far apart).

(b) Find the amount of energy required to exchange the positions of q1 and q2.

(c) Find the amount of energy required to exchange the positions of q1 and q3.

Four charges (q1 = +Q, q2 = +2Q, q3 = ?3Q, and q4 = +2Q,) are arranged as in the figure in the corners of a square with sides of length d. Find the total electric potential energy stored in this system (relative to U = 0 when they are at infinitely far apart). Find the amount of energy required to exchange the positions of q1 and q2. Find the amount of energy required to exchange the positions of q1 and q3.

Explanation / Answer

a) U = 2*k*Q^2/d + 2*k*Q^2/d - 3*k*Q^2/sqrt(2)*d +4*k*Q^2/sqrt(2)*d - 6*k*Q^2/d - 6*k*Q^2/d

   U = k*Q^2/d ( 2 + 2 - 3/1.414 + 4/1.414 - 6 - 6)
  
   U = (-7.29)*k*Q^2/d

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