Two charges of # 1 C # and # -2 C # are at points # (0,-1,2) # and # ( -2,5,7)#, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

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Answer 1 · 2017-07-18T22:36:01

#F_e = 2.77 xx 10^8# #"N"#

We're asked to find the magnitude of the electric force #F_e# between two point charges.

To do this, we can use the equation

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

where

#q_1# and #q_2# are the point charges (#1# #"C"# and #-2# #"C"#) , in no particular order
#k# is Coulomb's constant, equal to #8.988xx10^9("N"·"m"^2)/("C"^2)#
#r# is the distance between the two point charges, in #"m"#

This distance here can be found by the distance formula:

#r = sqrt((0-(-2))^2 + (-1-5)^2 + (2-7)^2)#

#= 8.06# #"m"#

Plugging in known values, we have

#F_e = (8.988xx10^9("N"·"m"^2)/("C"^2))(|(1cancel("C"))(-2cancel("C"))|)/((8.06cancel("m")^2))#

#= color(red)(2.77xx10^8# #color(red)("N"#