An infinite number of electric charges each equal to 5 nano coulombs are placed along x-axis at x = 1 cm, x-2 cm, x -4 cm, x = 8 cm,.. and so on. In this setup, if the consecutive charges have opposite sign, then the electric field in newton/coulomb at x =0 is

Options

A. `12 xx 10^(4)`
B. `24 xx 10^(4)`
C. `36 xx 10^(4)`
D. `48 xx 10^(4)`

Answer

( c)

Explanation

Net electric field intensity due to point charge is ,
`E = 1/ 4 pi epsilon_(0) [Q/r_(1)^(2) +Q/r_(2)^(2) + Q/r_(3)^(2) + Q/r_(4)^(2) + Q/r_(5)^(2)+……...]`
`= 9 xx 10^(9) xx5 xx 10^(-9)[1/1^(2) + 1/2^(2) + 1/4^(2) + 1/8^(2)+ ……..]`
` = 45/10^(-4)[1/1^(2) + 1/2^(2) + 1/4^(2) + 1/8^(2)+ …….]`
` = 45 xx 10^(4)|1/1^(2)/1 - (-1/2)^(2)|`
` = 1/1 + 1/4 = 4/5`
`:. E = 45 xx 10^(4) xx 4/5 = 36 xx 10^(4) N//C`