Two charges of # -1 C # and # -3 C# are positioned on a line at points # -5 # and # 2 #, respectively. What is the net force on a charge of # 4 C# at # 1 #?

1 Answer
Jan 13, 2017

Answer:

The net force is #1.07xx10^11N#, acting to the right.

Explanation:

We solve this problem by separately calculating the force acting on the #4C# charge due to each of the other two charges, then add them together. In this, I will assume the line referred to is measured in metres.

First, the force due to the #-1C# charge. I will call this #F_1#

#F_1=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(1)(4))/6^2=1xx10^9 N#

(Notice I have deliberately left out the signs on the charges. This is because I prefer to let the formulas determine the magnitude of the force. I already know the direction. Since these are unlike charges, they attract. So, #F_1# points toward the #-1C# charge - the to left.)

Next #F_3#, the force due to the #3C# charge

#F_1=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(3)(4))/1^2=1.08xx10^11 N#

This force acts toward the #-3C# charge, meaning to the right.

Since the two forces act in opposite directions, we subtract the two values to get the net force

#1.08xx10^11 N-1xx10^9N = 1.07xx10^11N#, acting to the right.