In the rectangle of the figure the sides have lengths 6.96 cm and 15.6 cm, q1 =
ID: 1436818 • Letter: I
Question
In the rectangle of the figure the sides have lengths 6.96 cm and 15.6 cm, q1 = -4.25 ?C, and q2 = +2.40 ?C. With V=0 at infinity, what is the electric potential at (a) corner A and (b) corner B? (c) How much work is required to move a charge q Subscript 3 Baseline ? equals plus 2.95 ?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-charge system? Is more, less, or the same work required if q3 is moved along a path that is (e) inside the rectangle but not on a diagonal and (f) outside the rectangle?
In case the image doesnt show, it is simply a horizontaly elongated rectagle with q1 in the upper left corner, a in the upper right corner, q2 in the lower right corner and b in the lower left corner.
Explanation / Answer
At corner A, the electric potential is the sum of contributions due to q1 and q2:
VA = k q1 / r1 + k q2 / r2
= k (q1 / r1 + q2 / r2)
= 9 x 10^9 [(-4.25 x 10^-6) / 0.156 + (2.40 x 10^-6) / 0.0696]
= 9 x 10^9 [- 2.724 x 10^-5 + 3.448 x 10^-5]
= 6.516 x 10^4 V
Similarly, at corner B, the electric potential is the sum of contributions due to q1 and q2:
VB = k q1 / r1 + k q2 / r2
= k (q1 / r1 + q2 / r2)
= 9 x 10^9 [(-4.25 x 10^-6) / 0.0696 + (2.40 x 10^-6) / 0.156]
= 9 x 10^9 [- 6.1 x 10^-5 + 1.538 x 10^-5]
= - 4.1 x 10^5 V
W = q3 * (VA - VB) = 2.95 x 10^-6 * (6.516 x 10^4 V - (- 4.1 x 10^5 V)) = 2.95 x 10^-6 (4.75 x 10^5) = 1.40 J
So work is positive, which means it increases the electric potential energy of the three-charge system.