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
Answer:
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((51)^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"" "))#