A charge of #2 C# is at #(-3 ,7)# and a charge of #-1 C# is at #( -3 ,5 )#. If both coordinates are in meters, what is the force between the charges?

1 Answer
Jun 7, 2017

Answer:

#4.49 xx 10^9# #"N"#

Explanation:

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

To find the magnitude of the force #F# (in #"N"#) between two point charges, we can use the equation

#F = k(|q_1q_2|)/(r^2)#

where

#8.988 xx 10^9 ("N" · "m"^2)/("C"^2)#

  • #q_1# and #q_2# are the two point charges (in #"C"#), in any order

  • #r# is the distance (in #"m"#) between the two charges

to find this, we simply find the distance between the two given coordinates:

#r = sqrt((-3 - -3)^2 + (7-5)^2) = color(red)(2# #color(red)("m"#

Plugging in our known values, we have

#F = (8.988 xx 10^9 ("N" · cancel("m"^2))/(cancel("C"^2)))(|(2cancel("C"))(-1cancel("C"))|)/((color(red)(2)cancel(color(red)("m")))^2)#

#= color(blue)(4.49 xx 10^9# #color(blue)("N"#