Question

Two charges are located on the positive x-axis of a coordinate system. Charge 𝑞1 = 2 × 10⁻⁹𝐶 is 2cm from the origin, and charge 𝑞2 = −3 × 10⁻⁹𝐶 is 4cm from the origin. What is the total force exerted by these two charges on a charge 𝑞3 = 5 × 10⁻⁹𝐶 located at the origin?

Answer 1

Solution.

$q_1=2\sdot10^{-9}C; r_1=0.02m;$

$q_2=-3\sdot10^{-9}C; r_2=0.04m;$

$F_{13}=k \dfrac{q_1\sdot q_3}{r_1^2};$

$F_{13}=9\sdot10^9\dfrac{2\sdot10^{-9}\sdot5\sdot10^{-9}}{0.02^2}=2.25\sdot10^{-4}N;$

$F_{23}=k\dfrac{q_2\sdot q_3}{r_2^2};$

$F_{23}=9\sdot10^9\dfrac{3\sdot10^{-9}\sdot5\sdot10^{-9}}{0.04^2}=0.84\sdot10^{-4}N;$

$F=F_{13}-F_{23}=2.25\sdot 10^{-9} - 0.84\sdot 10^{-9}=1.41\sdot10^{-9}N;$

Answer: $F=1.41\sdot10^{-9}N.$