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+q charges are placed at the points (1, 0), (2, 0), (4, 0), (8, 0) …. (up to infinity). What is the potential at the origin due to these charges?(a) \(\frac {2q}{3}\)(b) 2q(c) \(\frac {q}{3}\)(d) InfinityI got this question in class test.This is a very interesting question from Potential Energy of a System of Charges in portion Electrostatic Potential and Capacitance of Physics – Class 12

Answer»

Correct option is (b) 2q

The BEST explanation: Electric potential due to the CHARGES at the origin= q*\((\frac {1}{1} + \frac {1}{2} + \frac {1}{4} + \frac {1}{8} +…..=q*\frac {1}{1-\frac {1}{2}})\)=2q [by applying the formula of infinite G.P. series]. It can be shown that if the charges are alternately positive and negative, then the potential at the CENTER would be \(\frac {2q}{3}\) .



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