Three point charges are positioned at the corners of a rectangle as shown in the
ID: 1533888 • Letter: T
Question
Three point charges are positioned at the corners of a rectangle as shown in the figure. At the center of the rectangle, point A, the electric potential due to the three charges is zero (V_A = 0, relative to V = 0 at r = infinity) a. Calculate the value of the unknown charge Q_1 Make sure your calculation shows how you determine the sign as well as the magnitude of the charge. b. Calculate the electric potential (V_P) at the forth comer due to the three charges. c. Calculate the total electric potential energy of the system of three charges d. An electron moves from point A to point P. Calculate the electric potential difference through which the electron moves. Is it positive or negative? e. Calculate the change in the electric potential energy of the electron as it moves from A to P. Is it positive or negative? f. How much work is done by the electric forces as the electron moves from A to P? Is it positive or negative?Explanation / Answer
The problem can be solved as follows -
(a) Potential due to the three charges is ZERO.
So, 8.98 * 109 * 10-9 * (100/0.05 - 60/0.05 + Q3/0.05) = 0
=> Q3/0.05 = -800
=> Q3 = -800x0.05 = -40 nC
(b) Again, potential at fourth corner = 8.98 * 109 * 10-9 * (100/0.1 - 60/0.06 - 40/0.08)
= - 4490 V
(c) Potential energy of the system of the three charges -
= 8.98 * 109 * 10-18 * (- 100 * 60/0.08 - 100 * 40/0.06 + 60 * 40/0.1)
= - 1.056 * 10-3 J
(d) potential difference = - 4490 V. This is negative.
(e) Change in potential energy = 1.6 * 10-19 * 4490
= 7.184 * 10-16 J. This is positive.
Convert the value in eV = ( 7.184 * 10-16) / (1.6 x 10^-19) = 4490 eV
(f) Work done = - 7.184 * 10-16 J . The value is negative.
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