Problema cariche elettriche

Vedi al link:

RDOSSENA.ALTERVISTA.ORG "https://www.rdossena.altervista.org/2025-26/4B-Fis/2025-09-25-4B-Fis-es-legge-Coulomb.pdf"

F21 = 9*10^9*4*5*10^-20*10^4/3^2 = 2,00*10^-6 N

F23 = 9*10^9*3*5*10^-20*10^4/4^2 = 8,44*10^-7 N

F2 = √F21^2+F23^2 = 10^-6√2,00^2+0,844^2 = 2,17*10^-6 N

F12 = F21 = 2,00*10^-6 N

F13 = 9*10^9*3*4*10^-20*10^4/5^2 = 4,32*10^-7 N

F13y = F13*3/5 = 2,59*10^-7 N

F13x = F13*4/5 = 3,46*10^-7 N

F1 = √(F12+F13y)^2+F13x^2

F1 = 10^-6√(2,00+0,259)^2+0,346^2 = 2,29*10^-6 N 

a)...solo i moduli dei vettori...

F12 = k*Q1*Q2/a^2 = 9*10^9*4*5*10^-20/(3*10^-2)^2 = 2.*10^-6
F32 = k*Q3*Q2/b^2 = 9*10^9*3*5*10^-20/(4*10^-2)^2 = 8.4375*10^-7

F2 = sqrt(F12^2+F32^2)= 9*10^9*5*10^-10*sqrt((4*10^-10/(3*10^-2)^2)^2 + (3*10^-10/(4*10^-2)^2)^2) = ~ sqrt((2*10^-6)^2+(8.4375*10^-7)^2) = ~ 2.171*10^-6 N

b)

F21 = F12 = 2*10^-6 N

F31 = k*Q3*Q1/(sqrt(a²+b²))^2 = 9*10^9*3*4*10^-20/(5*10^-2)^2 = 4.32*10^-7 N

scelto x nella direzione di F21 sarà:

F21x = F21 ; F21y = 0 N

F31x = F31*cos(arccos(a/c)) = F31*3/5 = 2.592*10^-7 N

F31y = F31*cos(arccos(b/c)) = F31*4/5 = 3.456*10^-7 N

F1 = sqrt((F21x +F31x)^2+(F21y+F31y)^2) = sqrt((2*10^-6+2.592*10^-7)^2 + (0+3.456*10^-7)^2) =

= 2.285481... × 10^-6 = ~ 2.3*10^-6 N