(b) How much work must we do in order to bring in from infinitely far away a cha
ID: 1269068 • Letter: #
Question
(b) How much work must we do in order to bring in from infinitely far away a charge q2 = +2?C and place it at point 2? Will this increase or decrease the potential energy of the system? What is the potential energy of the system of the two charges?
(c) How much work must we do in order to bring in from infinitely far away a charge q3 = -3?C and place it at point 3? Will this increase or decrease the potential energy of the system? What is the potential energy of the system of the three charges?
(d) How much work must we do in order to bring in from infinitely far away a charge q4 = +4?C and place it at point 4? Will this increase or decrease the potential energy of the system? What is the potential energy of this final system of charges?
(e) Analyzing your work for the previous points, can you think of a shortcut for calculating the potential energy of the system of four charges? What is it?
Explanation / Answer
I am considering the magnitude of charges as micro coulomb.
(a) Electric Potential= kq/r
therefore, at point 2 , E.P= 8.987 * 10^9 * 1/6= 1.497 * 10^3 V
at point 3 , E.P= 8.987 * 10^9 * 1/4= 2.246 * 10^3 V
at point 4 , E.P= 8.987 * 10^9 * 1/7.211= 1.246 * 10^3 V
(b) Wok done to move charge from infinity to point 2 = q2 * potential at point 2
= 2 * 10^(-6) * 1.497 * 10^3
= 2.994 * 10^(-3) J
It will increase the potential energy of the system.
Potential Energy o the system= kq1q2/r
= 8.987 * 10^9 * 1 * 10^(-6) * 2 * 10(-6)/ 6
= 2.995 * 10^(-3) J
Similarly you can try other parts yourself, they all use exactly the same concepts.
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