# Two charges of # 9 C # and # 2 C# are positioned on a line at points # 4 # and # -4 #, respectively. What is the net force on a charge of # 3 C# at # -2 #?

##### 1 Answer

#### Answer:

#### Explanation:

The force between two charges is given by Coulomb's law:

#|vecF|=k(|q_1||q_2|)/r^2# where

#q_1# and#q_2# are the magnitudes of the charges,#r# is the distance between them, and#k# is a constant equal to#8.99xx10^9Nm^2//C^2# , sometimes referred to as Coulomb's constant.

Here is a quick diagram of the situation:

To find the net force on the

#vecF_(n e t)=sumvecF=vecF_(2 on 1)+vecF_(3 on 1)#

Recall that like charges repel, while opposite charges attract. Each of our charges are positive. Therefore, the force vectors can be drawn in as follows:

23 should say 21 in the above diagramwhere

#21 (23)# is the force of#q_1# on#q_2# and#31# is the force of#q_3# on#q_1#

So we can calculate

#|vecF_(31)|=k*(|q_1||q_3|)/(r_(31)^2)#

#=(8.99xx10^9Nm^2//C^2)*(3C*2C)/(2)^2#

#=1.35*10^(10)# #N#

#|vecF_(21)|=k*(|q_1||q_2|)/(r_(21)^2)#

#=(8.99xx10^9Nm^2//C^2)*(3C*9C)/(6)^2#

#=6.74*10^9# #N#

Therefore, we have:

#vecF_(n e t)=6.76*10^9# #N# (to the right)