What is the force between two small charged spheres having charges of 2 times 10^-72×107 C and 3 times 10^-73×107 C placed 30 cm apart in air?

1 Answer
Aug 3, 2017

F_"e" = 5.99xx10^-3Fe=5.99×103 "N"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)Fe=k|q1q2|r2

where

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

  • kk is Coulomb's constant, equal to 8.988xx10^9("N"·"m"^2)/("C"^2)8.988×109Nm2C2

  • q_1q1 and q_2q2 are the point charges (in coulombs), in no particular order

  • rr is the distance between the charges (in meters)

We have:

  • k = 8.988xx10^9("N"·"m"^2)/("C"^2)k=8.988×109Nm2C2

  • q_1 = 2xx10^-7q1=2×107 "C"C

  • q_2 = 3xx10^-7q2=3×107 "C"C

  • r = 30r=30 "cm"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"" ")|)