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an infinite number of charges each of magnitude q are placed along x axis at x=1, 2m, 4m, 8m, 16m and so on but the consecutive charges are of opposite signs starting with +q at m. A point charge Q kept at the origin experiences a force of magnitude...? Ans: qQ/ 5(pi)(E0) Can you please tell me how you get that answer?

an infinite number of charges each of magnitude q are placed along x axis at x=1, 2m, 4m, 8m, 16m and so on but the consecutive charges are of opposite signs starting with +q at m. A point charge Q kept at the origin experiences a force of magnitude...?
 
Ans:  qQ/ 5(pi)(E0)
 
Can you please tell me how you get that answer?

Grade:11

1 Answers

Pooja
127 Points
4 years ago

Force = kQ{q/r12 - q/r22 + q/r32 ........}
       = kqQ{ 1/12 - 1/22 + 1/42 - 1/ 82
          ..........}
       =kQq{1/1 - 1/4 + 1/16 - 1/64 ..........}

It's an infinite geometric progression


a = 1 (initial term)
r = -1/4 (common ratio)
S = a/(1-r)
   = 1÷ ( 1 + 1/4 ) = 4/5

 

 

So, Force = 4kQq/5
               = Qq/5π(epsilon)0

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