Question

An infinite number of electric charges each equal to 5 nano coulombs are placed along x-axis at x=1cm, x=2cm,x=4cm,x=8cm......and so on.in this setup if the consecutive charges have opposite sign then the electric field in Newton/coulomb at x=o is

Answer 1

Here q=5 *10^-9
E=Kq/r
Total E= E1+E2+E3....
= Kq/R1+ Kq/R2...
= Kq[1/R1+ 1/R2+.....]
= 9*10^9 * 5* 10^ -9[1/1*10-2+ 1/2*10-2+ 1/4*10-2+......]
so, the given series in the bracket is a geometric progression (GP) ,so it's sum will be 1/3
so, Total E = 9*10^9 * 5 *10-9*(1/3)
= 15 Newton/ coulomb.

Answer 2

Answer:

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