Two charges of # -1 C # and # -3 C # are at points # (-2 ,4,-3 ) # and # ( -3, 5,-81 )#, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

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Answer 1 · 2017-06-14T01:07:06

#4.41 xx 10^6# #"N"#

The electric force #F# between two point charges #q_1# and #q_2# separated by a distance #r# is given by the equation

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

where #k# is the Coulomb's law constant, equal to #8.988 xx 10^9 ("N"·"m"^2)/("C"^2)#

To find the distance between the two objects, we simply find the distance between the two coordinate points by

#r = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2)#

#= sqrt((-3"m"--2"m")^2 + (5"m"-4"m")^2 + (-81"m"--3"m")^2)#

#= color(red)(78.2# #color(red)("m"#

Since we have all our known variables, let's plug them in to the equation

#F = (8.988 xx 10^9 ("N"·cancel("m"^2))/(cancel("C"^2)))((|(-1cancel("C"))(-3cancel("C"))|)/(color(red)(78.2)cancel(color(red)("m")))^2)#

#= color(blue)(4.41 xx 10^6# #color(blue)("N"#