Answer to Question #96390 in Electricity and Magnetism for Lawal adedamola olumide

Question

Calculate the magnitude and direction of the resultant force of charge q4 due to the three other charges. Q1=-16microcoloumbs, q2=15microcoloumbs, q3= -8microcoloumbs, q4= -5microcoloumbs. Distance between q1 and q4 is 0.4m, and the distance between q3 and q4 is 0.3m

Answer 1

The resultant force can be calculated as a sum of all forces acting on the given charge according to Coulomb's law:

$$F_{14}=k\frac{q_1q_4}{r_{14}^2}=9\cdot10^9\cdot\frac{(-16)\cdot10^{-6}(-5)\cdot10^{-6}}{0.4^2}=4.5\text{ N}.$$

$$F_{24}=k\frac{q_2q_4}{r_{24}^2}=9\cdot10^9\cdot\frac{15\cdot10^{-6}(-5)\cdot10^{-6}}{r_{24}^2}=-\frac{0.675}{r_{24}^2}\text{ N}.$$

$$F_{34}=k\frac{q_3q_4}{r_{34}^2}=9\cdot10^9\cdot\frac{(-8)\cdot10^{-6}(-5)\cdot10^{-6}}{0.3^2}=4\text{ N}.$$

$$F_{net}=F_{14}+F_{24}+F_{34}=4.5-\frac{0.675}{r_{24}^2}+4=\bigg(8-\frac{0.675}{r_{24}^2}\bigg)\text{ N}.$$