Two charges of # 5# # C # and # -1# # C# are positioned on a line at points # -2 # and # 1 #, respectively. What is the net force on a charge of # 1# #C# at # -1 #?

1 Answer
Jul 15, 2017

Answer:

#F_"net" = 4.725xx10^10# #N# in the positive direction.

Explanation:

If we imagine the situation (or, better, draw a large, clear, labeled diagram!) we know that the #5# #C# charge is #1# #m# from the #1# #C# charge and the #-1# #C# charge is #2# #m# from it in the opposite direction.

(We were not told the units of distance on the line but we need to assume it was #m# to be able to solve the problem)

It's also worth realising that the force on the #1# #C# charge due to the #5# #C# charge will be large and repulsive (i.e. in the positive direction along the line), and the force on it due to the #-1# #C# charge will be smaller but attractive and therefore also in the positive direction.

#F=(kq_1q_2)/r^2#

For the #5# #C# charge:

#F=(9xx10^9xx5xx1)/1^2=4.5xx10^10# #N# in the positive direction.

(if we drew our number line in the usual left-to-right direction, this force is acting to the right)

For the #-1# #C# charge:

#F=(9xx10^9xx-1xx1)/2^2=2.25xx10^9# #N#, also in the positive direction

The net force is simply the sum of these two forces:

#F_"net" = 4.5xx10^10 + 2.25xx10^9 = 4.725xx10^10# #N# in the positive direction.