Question

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

Answer 1

`"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.

• 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`

• 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.

• `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"`