What's the force on charge Q3? Thank you!

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1 Answer
Apr 25, 2018

#"The force on charge "Q_3 " is 153.75 Newtons." #

Explanation:

it will be useful to remember the fallowing basic information.

  • there are two kind of electrical charges(positive and negative.
  • the source of positive electrical charges is proton.
  • the source of negative electrical charges is electron.
  • Electric charges apply mutually force to each other.
  • if two electrical charges have the same sign, they will push each other.

  • if two electrical charges have the different sign, they will pull each other.

  • The force between two electrical charge is calculated using Coulomb's law.

  • The electrical charge unit is Coulomb(C).

#F=k*(q_1*q_2)/r^2#

  • The force is directly proportional to the product of the electrical charges.
  • The force is inversely proportional to the square of the distance between the electrical charges.

  • Force is a vector quantity. We will symbolize each force by drawing a vector.

  • #" "1 " "cm=10^(-2) m#

  • #" "1" " mu C=10^(-6) C#

now we can solve the problem.

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  • The #color(red)( F_1)# vector indicates the pushing force between the electrical charges Q1 and Q3.

#color(red)(F_1)=9*10^9*(50*10^-6*30*10^-6)/((30*10^-2)^2)=(cancel(9)*15*10^-1)/(cancel(9)*10^-2)=150N#

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  • The #color(blue)( F_2)# vector indicates the pulling force between the loads Q2 and Q3.

#color(red)(F_2)=9*10^9*(-20*10^-6*30*10^-6)/((40*10^-2)^2)=-(54*10^-1)/(16*10^-2)=-33,75N#

  • Now we have to find the vector sum of two forces.

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  • # vec F_1 +vec F_2=vec F" (vector notation display)"#

  • the magnitude of vector can be calculated using pythagorean theorem

#|F|=sqrt(color(red)(F_1)^2+color(blue)(F_2)^2)#

#F=sqrt(150^2+(-33.75)^2)#

#F=sqrt(22500+1139.06)#

#F=sqrt(23639.06)#

#F=153.75" N"#