A 1C charge is placed at the origin. Other infinite numbers of unit charges are placed at ?2, ?4, ?8, ?16,….(up to infinite) distances from the origin in a straight line. What will be the total force acting on the 1st charge?
A. 9*109 N
B. 18*109 N
C. Infinite
D. 1 N
Answer:A
A 1C charge is placed at the origin. Other infinite numbers of unit charges are placed at ?2, ?4, ?8, ?16,….(up to infinite) distances from the origin in a straight line. What will be the total force acting on the 1st charge?
A. 9*109 N B. 18*109 N C. Infinite D. 1 N
Explanation: The force on 1st charge will be = 9*10-9*(\(\frac {1}{\sqrt{2}^2} + \frac {1}{\sqrt{4}^2} + \frac {1}{\sqrt{8}^2}\) +?) = 9*10-9*\(\frac {\frac {1}{2}}{1-\frac {1}{2}}\) = 9*10-9N [infinite GP formula].