Problema fisica campo elettrico

Q(Α)= 7·10^(-9) C in A [4 m, 2.5m]

Q(Β) = - 5.2·10^(-9) C in Β [-2 m, -3 m]

Campo elettrico in P:

P [-1m , 1 m]

rΑ = (-1 - 4)·i + (1 - 2.5)·j----> rΑ = - 5·i - 3·j/2

rΒ = (-1 + 2)·i + (1 + 3)·j----> r·Β = i + 4·j

rΑ = √((-5)^2 + (- 3/2)^2)-----> r·Α = 5.22 m

rΒ = √(1^2 + 4^2)-----> rΒ = 4.12 m

Κo = 8.987·10^9·Ν·m^2/C^2  (costante elettrostatica nel vuoto)

ΕΑ = 8.987·10^9·7·10^(-9)/5.22^3·(- 5·i - 3/2·j)

EA = - 2.211·i - 0.663·j

ΕΒ = 8.987·10^9·(- 5.2·10^(-9))/4.12^3·(i + 4·j)

EB = - 0.668·i - 2.673·j

ΕΡ = ΕΑ + ΕΒ = (- 2.211·i - 0.663·j) + (- 0.668·i - 2.673·j)

ΕΡ = ΕΑ + ΕΒ = - 2.879·i - 3.336·j

ΕΡ = √((-2.879)^2 + (-3.336)^2)----> ΕΡ = 4.407 N/C

... le distanze da P

d1 = sqrt((4 + 1)^2 + (2.5 - 1)^2) = 5.220153...

d2 = sqrt((-1 + 2)^2 + (1 + 3)^2) = sqrt17 = 4.1231...

i moduli dei campi in P:

E1 = k*qa/d1² ~ 2.312 N/C verso soo

E2 = k*qb/d2² = ~ 2.75308 N/C verso sso

-E1x = E1*cos(arctan((ya-yp)/(xa-xp))) = ~ 2.312*cos(arctan(1.5/5) ) = ~ 2.2145

-E1y = E1*sin(arctan((ya-yp)/(xa-xp))) = ~ 2.312*sin(arctan(1.5/5)) = ~ 0.664

-E2x = E2*cos(arctan((yb-yp)/(xb-xp))) = ~ 2.7531*cos(arctan(4/1)) = ~ 0.6677

-E2y = E2*sin(arctan((yb-yp)/(xb-xp))) = ~ 2.7531*sin(arctan(4/1)) = ~ 2.671

-Ex = ~ 2.8815 N/C ---> Ex = ~ - 2.9 N/C

-Ey = ~  3.335 N/C ---> Ey = ~ - 3.335 N/C

E =  sqrt(Ex^2 + Ey^2) = ~ sqrt(2.8815^2 + 3.335^2) = 4.40741049... = ~ 4.4 N/C