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?

1 Answer
Aug 3, 2017

#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"" ")|)#