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 #?

Question

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   #?

Adrian Ayala · Accepted Answer

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

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. We deduct the two values to obtain the net force because the two forces act in opposing directions. #1.08xx10^11 N-1xx10^9N = 1.07xx10^11N#, acting to the right.

Julia Aguilar · Answer

undefined Net force = $ k \cdot \frac{q_1 \cdot q_2}{r^2} $
$k = 8.99 \times 10^9 \ \text{N m}^2/\text{C}^2$
$q_1 = -1 \ \text{C}$, $q_2 = -3 \ \text{C}$, $q_3 = 4 \ \text{C}$
$r_1 = 6 \ \text{m}$, $r_2 = 1 \ \text{m}$
Calculate the forces between each pair of charges, then find the net force by summing these individual forces.