Question

A charge of `1 C` is at `(-5 ,-2 ,7 )` and a charge of `2 C` is at `(0,8,4)`. If both coordinates are in meters, what is the force between the charges?

Answer 1

Force between charges is `1.343⋅10^8` Newton

Explanation:

Distance `d` between `(x_1,y_1,z_1)` and `(x_2,y_2,z_2)` is given by

`sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`.

In the instant case, this turns out to be `sqrt((0+5)^2+(8+2)^2+(4-7)^2)`, which simplifies to `sqrt(25+100+9)` or `sqrt134`.

The force between two charges `C_1` and `C_2` is given by `k*(C_1*C_2)/d^2`, where `k` is Coulomb's law constant for the medium between the charges and for air it is `9*10^9 Nm^2/C^2`, where charge is in Coulomb and distance in meters.

Assuming it to be so Force will be given by

`9*1*2/134*10^9` or `1.343*10^8` Newton.