Question

Two charges of `-7 C` and `4 C` are at points `(4, 7 ,-8)` and `( -1 , 3, -8 )`, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

Answer 1

The force is `-0.25*10^12` N.

Explanation:

The Coulomb force is

`F=1/(4pi epsilon_0)(Q_1 Q_2)/r^2`. The only unknown quantity is `r`, the distance between the two charges.
We can calculate using the Pitagora's theorem in three dimensions:

`r=sqrt((x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2)=sqrt((4+1)^2+(7-3)^2+(-8+8)^2)= sqrt(5^2+4^2+0^2)=sqrt(5^2+4^2+0^2)=sqrt(41)`.

The force is

`F=1/(4pi epsilon_0)(Q_1 Q_2)/r^2=1/(4*3.14*8.854*10^-12)*((-7)*4)/(41)=-(28*10^12)/(4*3.14*8.854)=`
`-(28*10^12)/111.20624=-0.25*10^12` N.
The minus sign means that the two charges are attracting each other.