In the rectangle of the figure the sides have lengths 6.65 cm and 17.3 cm, q_1 =
ID: 1531597 • Letter: I
Question
In the rectangle of the figure the sides have lengths 6.65 cm and 17.3 cm, q_1 = -5.65 mu C, and q_2 = +2.43 mu C. With V = 0 at infinity, what is the electric what is the electric potential at a corner A and b corner B c how much work is required to move a change Q_3 = +3.00 mu C from B to A along a diagonal of the rectangle d) Does this work increase or decrease the electric potential energy of the three change system? Is more, or the same work required if q_3 is moved along a path that is c) inside the rectangle but not on a diagonal and f) outside the rectangle?Explanation / Answer
At corner A, the electric potential is the sum of contributions due to q1 and q2:
VA = kq1 / r1 + kq2 / r2
VA = k (q1 / r1 + q2 / r2)
VA = (9 X 10^9) [-5.65 X 10^-6 / 0.173 + 2.43 X 10^-6 / 0.0665]
VA = (9 x 10^9) [-3.266 x 10^-5 + 3.654 x 10^-5]
VA = 3.492 x 10^4 V
Similarly, at corner B, the electric potential is the sum of contributions due to q1 and q2:
VB = kq1 / r1 + kq2 / r2
VB = k (q1 / r1 + q2 / r2)
VB = (9 X 10^9) [-5.65 X 10^-6 / 0.0665 + 2.43 X 10^-6 / 0.173]
VB = (9 x 10^9) [-8.5 x 10^-5 + 1.4 x 10^-5]
VB = -6.39 x 10^5 V
c)
W = q3*(VA - VB)
W = (3 x 10^-6)*((3.492 x 10^4 V) - (-6.39 x 10^5 V))
W = 2.02 J
So work is positive, which means it increases the electric potential energy of the three-charge system