A charge of #2 C# is at #(-4, -1 )# and a charge of #-1 C# is at #( 2,-5 )#. If both coordinates are in meters, what is the force between the charges?

1 Answer
Jul 11, 2017

Answer:

#3.46 xx 10^8# #"N"#

Explanation:

We're asked to find the magnitude of the electric force #F_e# between two point charges, which we'll call #q_1# and #q_2#.

To do this, we can use the equation

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

where

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

  • #r# is the distance, in #"m"#, between the point charges

This distance is found via the distance formula:

#r = sqrt((-4-2)^2 + (-1-(-5))^2) = color(red)(7.21# #color(red)("m"#

Plugging in known values, we have

#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)(3.46xx10^8# #color(blue)("N"#