In the rectangle of the figure the sides have lengths 5.14 cm and 14.2 cm, q_1 =
ID: 1535232 • Letter: I
Question
In the rectangle of the figure the sides have lengths 5.14 cm and 14.2 cm, q_1 = -4.23 mu C_1 and q_2 = + 1.65 mu 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_3 = + 3.08 mu C from B to A along a diagonal of the rectangle? (d) Does this week 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? _______________ Units _______________ Units _______________ UnitsExplanation / Answer
(a)
At corner A, the electric potential is the sum of contributions due to q1 and q2:
VA = k q1 / r1 + k q2 / r2
VA = k (q1 / r1 + q2 / r2)
VA = 9 x 109 [-4.23 x 10-6 / 0.142 + 1.65 x 10-6 / 0.0514]
VA = 9 x 109 [-2.9788 x 10-5 + 3.21 x 10-5]
VA = 2.097 x 104 V
(b)
Similarly, at corner B, the electric potential is the sum of contributions due to q1 and q2:
VB = k q1 / r1 + k q2 / r2
VB = k (q1 / r1 + q2 / r2)
VB = 9 x 109 [-4.23 x 10-6 / 0.0514 + 1.65 x 10-6 / 0.142]
VB = 9 x 109 [-8.2295 x 10-5 + 1.1619 x 10-5]
VB = 9 x 109 [-7.0676 x 10-5]
VB = -6.36 x 105 V
(c)
W = q3 * (VA - VB)
W = 3.08 x 10-6 * (2.097 x 104 V - (-6.36 x 105 V))
W= 2.023 J
(d)
W= +2.023 J
work is positive, which means it increases the electric potential energy of the three-charge system.
Choose answer: More Work required
(e)
The Electrostatic force is conservative, so the work is the same no matter which path is used
Choose Answer: Same Work
(f) The Electrostatic force is conservative, so the work is the same no matter which path is used
Choose Answer: Same Work