What's the force on charge Q3?
1 Answer
Explanation:
The force between two point charges is given by Coulomb's Law:
#color(blue)(F=1/(4piepsilon_0)*(abs(q_1)abs(q_2))/r^2)# where
#r# is the distance between the charges
To find the net force on
We have the following information:
#Q_1=-50muC# #Q_2=100muC# #Q_3=-20muC# #r_(12)=20.0"cm"# #r_(13)=40.0"cm"# #epsilon_0=8.85 10^(−12)" C"^2//"Nm"^2#
Let's start with
#Q_1# and#Q_3# are both negative charges. Therefore the charges repel, and the force exerted on#Q_3# by#Q_1# points to the right.
#F_(13)=1/(4piepsilon_0)*(abs(-50*10^-6C)abs(-20*10^-6C))/(40.0*10^-2m)^2#
#=>~~56"N"# (to the right)
Now we can calculate the force between
#Q_2# is a positive charge, whereas#Q_3# is a negative charge. Therefore the charges attract, and the force exerted on#Q_3# by#Q_2# is to the left.
#F_(23)=1/(4piepsilon_0)*(abs(100*10^-6C)abs(-20*10^-6C))/(20.0*10^-2m)^2#
#=>~~450"N"# (to the left)
- Then, since the charges are all placed along a straight line, we can simply add these values for force together to get the net force.
- However, note that these are forces and do have directions associated with them. We can already see that the net force will be to the left, as this is is a much greater value than that to the right.
- We will therefore subtract
#F_(13)# from#F_(23)# .
#F_(" on "Q_3)=450"N"-56"N=394"N"#
That is,
Alternatively, you can define left as the negative direction and make the calculated force net negative. Then upon adding the two forces you would obtain a negative net force, which indicates that the net force is to the left.