Two charges of # -2 C # and # -3 C# are positioned on a line at points # 4 # and # -1 #, respectively. What is the net force on a charge of # 5 C# at # 0 #?

1 Answer
Nov 7, 2017

Answer:

#115/8k_eC^2# to the negative direction.

Explanation:

Electrostatic force between two point charges can be calculated using Coulomb's law.
#F=k_e(q_1*q_2)/r^2#, where #k_e# is the Coulomb's constant(#k=8.99*10^9 Nm^2C^-2#), #q_1# and #q_2# are the charges and #r# is the distance.

Force between #-2C# (at the point 4) and #5C# (at the point 0) is
#F_1=k_e(2C*5C)/4^2=5/8k_eC^2#. The direction of #F_1# is positive, for the two point charges have opposite signs.

Force between #-3C# (at the point -1) and #5C# (at the point 0) is
#F_2=k_e(3C*5C)/1^2=15k_eC^2#. This is also an attractive force, so the direction is negative.

Therefore, the net force on a charge of #5C# at #0# is #15k_eC^2-5/8k_eC^2=115/8k_eC^2#, and its direction is negative.