Question

A charge of `1 C` is at `(-2,7,1)` and a charge of `2 C` is at `(8,-1,4)`. If both coordinates are in meters, what is the force between the charges?

Answer 1

`F=1.04times10^8 N`

Explanation:

Charge `1C` placed at `(-2,7,1)`
Charge `2C` placed at `(8,-1,4)`

Distance between the charges
`r=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`
`r=sqrt((8-(-2))^2+((-1)-7)^2+(4-1)^2`
`r=sqrt((8+2)^2+(-1-7)^2+(4-1)^2)`
`r=sqrt(10^2+(-8)^2+(3)^2)`
`r=sqrt(100+64+9)=sqrt(173)`

Force between charges
`F=(kq_1q_2)/r^2`
where `k=9times10^9 N-m^2/C^2`

`F=(9times10^9times1times2)/(sqrt173)^2`
`F=(18times10^9)/173=0.104times10^9`
`F=1.04times10^8 N`