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

electric potential energy = k*q1*q2/r

electric potential energy of system= k*Q*2Q/d + k*Q*2Q/d - k*Q*3Q/sqrt(2)*d

electric potential energy of system when q1 q2 interchanged= k*Q*2Q/d - k*Q*3Q/d + k*Q*2Q/sqrt(2)*d

energy required= change in potential energy in both config= -k*Q*Q/d - k*Q*Q/sqrt(2)*d

electric potential energy of system when q1 q3 interchanged= k*Q*2Q/d + k*Q*2Q/d - k*Q*3Q/sqrt(2)*d

energy required= 0 (similar config after interchanging too)

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