A charge of #2 C# is at #(-9,1 )# 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
May 30, 2017

Answer:

#1.15 xx 10^8 "N"#

Explanation:

The electric force #F# (in #"N"#) between two point charges #q_1# and #q_2# (in #"C"#) is represented by the equation

#F = 1/(4piepsilon_0)(|q_1q_2|)/(r^2)#

where

  • #epsilon_0# is a physical constant called the permittivity of free space, equal to #8.8542 xx 10^-12 (C^2)/(N*m^2)#, and

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

To find the distance between the two charges, we can use the distance formula:

#r = sqrt((1--5)^2 + (-9-2)^2) = color(red)(12.5"m"#

Now that we have all the necessary variables, let's plug them into the equation to find the charge:

#F = 1/(4pi(8.8542 xx 10^-12 (cancel(C^2))/(N*cancel(m^2))))(|(2cancel("C"))(-1cancel("C"))|)/((12.5cancel("m"))^2)#

#= color(blue)(1.15 xx 10^8 "N"#

Thus, the electric force between the two point charges is #1.15 xx 10^8 "N"#, and since the charges are opposite, the force is that of attraction.