Question

What is the force between two small charged spheres having charges of `2 times 10^-7` C and `3 times 10^-7` C placed 30 cm apart in air?

Answer 1

`F_"e" = 5.99xx10^-3` `"N"`

Explanation:

We're asked to find the magnitude of the electric force between two point charges.

To do this, we can use the equation

`F_"e" = k(|q_1q_2|)/(r^2)`

where

• `F_"e"` is the magnitude of the electric force (in newtons)

• `k` is Coulomb's constant, equal to `8.988xx10^9("N"·"m"^2)/("C"^2)`

• `q_1` and `q_2` are the point charges (in coulombs), in no particular order

• `r` is the distance between the charges (in meters)

We have:

• `k = 8.988xx10^9("N"·"m"^2)/("C"^2)`

• `q_1 = 2xx10^-7` `"C"`

• `q_2 = 3xx10^-7` `"C"`

• `r = 30` `"cm"` `= ul(0.30color(white)(l)"m"`

Plugging in known values:

`F_"e" = (8.988xx10^9("N"·cancel("m"^2))/(cancel("C"^2)))(|(2xx10^-7cancel("C"))(3xx10^-7cancel("C"))|)/((0.30cancel("m"))^2)`

`= color(red)(ulbar(|stackrel(" ")(" "5.99xx10^-3color(white)(l)"N"" ")|)`