Two charges of # 2 C # and # 3 C# are positioned on a line at points # -5 # and # 6 #, respectively. What is the net force on a charge of # -8 C# at # -2 #?

1 Answer
Dec 25, 2015

Answer:

Let us use Coulomb's Law for electrostatic interaction.

Explanation:

Charges distribution is given by this picture:

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where blue charges will be our fonts, and the red charge will be our object charge.

According to Coulomb's Law, the force between two charges 1 and 2 is given by:

#F_{12} = {1}/{4 pi varepsilon_0} {q_1 cdot q_2}/{d^2} = K {q_1 cdot q_2}/{d^2}#

where #K = 9 cdot 10^9 "N" cdot "m"^2 / "C"^2# is electrostatic constant, #q_1# and #q_2# are the values of charges in coulombs, and #d# is the distance between both charges.
Electrostatic force is repulsive if both charges have the same sign, and attractive if they have opposite signs.

Let us calculate both forces:

  • Force from 1 to 3:

#F_{13} = 9 cdot 10^9 "N" cdot "m"^2 / "C"^2 cdot {2 "C" cdot (-8) "C"}/(3 "m")^2 = -16 cdot 10^9 "N"#

  • Force from 2 to 3:

#F_{23} = 9 cdot 10^9 "N" cdot "m"^2 / "C"^2 cdot {3 "C" cdot (-8) "C"}/(8 "m")^2 = -3,375 cdot 10^9 "N"#

Both forces are attractive (that's why both signs are negative). We must substract them, and the resultant force has the same orientation than the bigger one:

#F_"Total" = (16 cdot 10^9 "N") - (3,375 cdot 10^9 "N") = 12,625 cdot 10^9 "N"#

#vec F_"Total"# goes from charge 3 to charge 1 (because #F_{13}# is bigger than #F_{23}#)