At some distance from a particles with the charge of 9 nC the electric field of the charge has a magnitude of 81 N/C. At what distance from the particle does electric field have a magnitude three...

At some distance from a particles with the charge of 9 nC the electric field of the charge has a magnitude of 81 N/C. At what distance from the particle does electric field have a magnitude three times smaller?

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Electric field created by a point charge by using the equation

`E=(kQ)/r^2`         (i)

where   Q=`9.0xx10^(-6) C`

r=distance between charges

k (universal constant)=`9.0xx10^9 (Nm^2)/C^2`

`E=81N/C`

`81=(9xx10^9)xx(9xx10^(-6)}/r^2`

`` `r^2=10^3`

`r=sqrt(1000)`       (ii)

Let harge is place at a distance of `r_1`  ,so electrical field is E/3.

So

`E/3=kQ/r_1^2`         

`E=(3kQ)/r_1^2`              (ii)

from (i) and (ii)

`(3kQ)/r_1^2=(kQ)/r^2`

`r_1^2=3r^2`

`r_1=sqrt(3)r`

`r_1=sqrt(3000)` m

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