A charge of #-2 C# is at #(-5 , 1 )# and a charge of #-1 C# is at #(1 ,-3) #. If both coordinates are in meters, what is the force between the charges?

1 Answer
Aug 7, 2017

Answer:

#F_"e" = 3.46xx10^8# #"N"#

Explanation:

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

To do this, we can use Coulomb's law:

#ulbar(|stackrel(" ")(" "F_"e" = k(|q_1q_2|)/(r^2)" ")|)#

where

  • #F_"e"# is the magnitude of the electric force

  • #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 no particular order

  • #r# is the distance, in meters, between the two point charges

We have:

  • #k = 8.988xx10^9("N"*"m"^2)/("C"^2)#

  • #q_1 = -2# #"C"#

  • #q_2 = -1# #"C"#

  • to calculate #r#, we use the distance formula:

#r = sqrt((-5-1)^2 + (1-(-3))^2) = color(red)(ul(7.21#

Plugging these in:

#F_"e" = 8.988xx10^9("N"*cancel("m"^2))/(cancel("C"^2))((|(-2cancel("C"))(-1cancel("C"))|)/((color(red)(7.21)cancel(color(red)("m")))^2)) = color(blue)(ulbar(|stackrel(" ")(" "3.46xx10^8color(white)(l)"N"" ")|)#