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

1 Answer
Jan 28, 2017

Answer:

The net force will be #4.50 xx10^9N# acting to the right (toward the #-3C# charge at -1.

Explanation:

We solve this problem by separately calculating the force acting on the #-3C# 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 #-4C# charge. I will call this #F_4#

#F_4=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(3)(4))/4^2=6.75xx10^9 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 like charges, they repel. So, #F_4# points away from the #-4C# charge - the to right.)

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

#F_3=(1/(4pi epsilon_o)) ((q_1q_2)/r^2) = ((9xx10^9)(3)(3))/6^2=2.25xx10^9 N#

This force also repels the -3C charge at -1, meaning it acts to the left.

Since the two forces act in opposite directions, we subtract the two values to get the net force. Since #F_4# is the greater force, the net force acts to the right.

#6.75xx10^9 N-2.25xx10^9N = 4.50xx10^9N#