Geometria Analitica

13)

^ = ESCALAR

FAB = I x L1 ^ B

FAB = 4 x 0,3 k ^ 0,5 j

FAB = 1,2 k ^ 0,5 j

FAB = - 0,6 i N

FBC = I x L2 ^ B

FBC = 4 x 0,2 j ^ 0,5 j

FBC = 0

21)

Eaq1 = L x Q1 / r²

Eaq1 = 9 x 10 ^ 9 x - 12,5 x 10 ^ (-6) / 0,15² = -5x10^6 V/m

Eaq2 = L x Q1 / r²

Eaq2 = 9 x 10 ^ 9 x -25 x 10 ^ (-6) / 0,10² = -2,25x10^7 V/m

Ea = Eaq1 - Eaq2 = -5x10^6 - (-2,25x10^7) = 1,75 x 10 ^ 7 i V/m

Ebq1 = L x Q1 / r²

Ebq1 = 9 x 10 ^ 9 x -12,5 x 10 ^ (-6) / 0,10² = -1,125x10^7 V/m

Ebq2 = L x Q1 / r²

Ebq2 = 9 x 10 ^ 9 x -25 x 10 ^ (-6) / 0,35² = -1,84x10^6 V/m

Eb = Ebq1 + Ebq2 = -1,125x10^7 - (-1,84x10^6) = 1,309 x 10 ^ 7 i V/m

F = q x E

Fa = q x Ea

Fa = 4 x 10 ^ (-3) x 1,75 x 10^7 = 7 x 10 ^ 4 i N

Fb = q x Eb

Fb = 4x10^(-3) x 1,309x10^7 = 5,236 x 10 ^ 4 i N

28)

VP = L x (qa/"AP" + qb/"BP" + qc/"CP")

VP = 9x10^9 x (4x10^(-6)/11 + (-2x10^(-6))/10 + 6x10^(-6)/45^(1/2))

VP = 9x10^9 x (3,64x10^(-7) - 2x10^(-7) + 8,94x10^(-7))

VP = 9x10^9 x 1,0584x10^(-6)

VP = 9,522x10^3 V

V0 = L x (qa/"A0" + qb/"B0" + qc/"C0")

V0 = 9x10^9 x (4x10^(-6)/5 + (-2x10^(-6))/8 + 6x10^(-6)/3)

V0 = 9x10^9 x (8x10^(-7) - 2,5x10^(-7) + 2x10^(-6))

V0 = 9x10^9 x 2,55x10^(-6)

V0 = 2,295x10^4 V

τP0 = q x (VP - V0)

τP0 = -0,5x10^(-6) x (9,522x10^3 -2,295x10^4)

τP0 = 6,714x10^(-3) J