Two charges of # 2 C # and # 8 C# are positioned on a line at points # -3 # and # 6 #, respectively. What is the net force on a charge of # -3 C# at # -2 #?

1 Answer
Feb 3, 2016

Answer:

#Delta F=50,625*10^9*C^2#

Explanation:

![enter image source here]
#q_a=2C# charge on the point of A
#q_b=-3C# charge on the point of B
#q_c=8C# charge on the point of C
#k=9*10^9 (N*m^2)/C^2#
#"formula needed to solve this problem is Coulomb's law"#
#F=k*(q_1*q_2)/d^2 #
# F: "Force between two charges acting each other"#
#q_1,q_2: "charges" #
#d:"distance between two charges"#

#step:1#
#color(red)(F_(AB))=k*(q_A*q_B)/(d_(AB)^2#
#color(red)(F_(AB))=9*10^9(2C*(-3C))/1^2#
#color(red)(F_(AB))=-54*C^2*10^9#

#step:2#
#color(blue)(F_(CB))=k*(q_C*q_B)/(d_(CB)^2#
#color(blue)(F_(CB))=9*10^9(cancel(8)C*(-3C))/cancel(8)^2#
#color(blue)(F_(CB))=-27*10^9*C^2/8#
#color(blue)(F_(CB))=-3,375*10^9*C^2#

#step:3#
#Delta F=color(blue)(F_(CB))-color(red)(F_(AB))#
#Delta F=-3,375*10^9*C^2-(-54*10^9*C²)#
#Delta F=-3,375*10^9*C^2+54*10^9*C^2#
#Delta F=50,625*10^9*C^2#