Two charges of # -7 C # and # 4 C # are at points # (4, 7 ,-8) # and # ( 2 ,-3, -8 )#, respectively. Assuming that both coordinates are in meters, what is the force between the two points?

1 Answer
Jul 10, 2017

Answer:

#F_e = 2.42 xx 10^9# #"N"#

Explanation:

We're asked to find he magnitude of the electric force #F_e# between two point charges, which we'll call #q_1# and #q_2#.

To do this, we can use the equation

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

where

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

  • #r# is the distance between the two point charges, in #"m"#

This distance can be found via the distance formula:

#r = sqrt((4-2)^2 + (7-(-3))^2 + (-8-(-8))^2) = color(red)(10.2# #color(red)("m"#

Plugging in known values, we have

#F_e = (8.988 xx 10^9("N"•cancel("m"^2))/(cancel("C"^2)))((|(-7cancel("C"))(4cancel("C"))|)/((color(red)(10.2)cancel(color(red)("m")))^2))#

#= color(blue)(2.42xx10^9# #color(blue)("N"#