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
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"" ")|)#
