Two charges of # 3 C # and # -7 C# are positioned on a line at points # 6 # and # 5 #, respectively. What is the net force on a charge of # 2 C# at # -2 #?

1 Answer
May 13, 2017

Answer:

#vecF_(n e t)=1.12xx10^10# #N#

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:

enter image source here

To find the net force on the #2C# charge, we consider the force exerted on it by the #-7C# and #3C# charges. Let's call the #2C# charge #q_1#, the #-7C# charge #q_2# and the #3C# charge #q_3#. Then:

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

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

enter image source here

So we can calculate #vecF_(21)# and subtract from that #vecF_(31)# to find the net force on the #q_1# charge.

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

#=(8.99xx10^9Nm^2//C^2)*(7C*2C)/(7)^2#

#=2.57*10^9# #N#

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

#=(8.99xx10^9Nm^2//C^2)*(3C*2C)/(8)^2#

#=8.43*10^8# #N#

Therefore, we have:

#vecF_(n e t)=1.73*10^9# #N#