Question

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`?

Answer 1

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

Explanation:

`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`