Two charges of $- 1 C$ $-1 C$ and $- 2 C$ $-2 C$ are positioned on a line at points $- 6$ $-6$ and $4$ $4$ , respectively. What is the net force on a charge of $3 C$ $3 C$ at $1$ $1$ ?

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Two charges of $- 1 C$ $-1 C$ and $- 2 C$ $-2 C$ are positioned on a line at points $- 6$ $-6$ and $4$ $4$ , respectively. What is the net force on a charge of $3 C$ $3 C$ at $1$ $1$ ?

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Answer 1 · 2016-05-14T20:01:34

${\to F}_{R} = - 5.45 \cdot 10^{9} N attractive force$ $vec F_R=-5.45*10^9" "N" attractive force"$

Explanation:

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$data given:$ $"data given:"$

$k = {9.10}^{9} N \cdot m^{2} \cdot C^{- 2}$ $k=9.10^9 N*m^2*C^-2$

$F = k \cdot \frac{Q_{1} \cdot Q_{2}}{r^{2}} Coulomb's law$ $F=k*(Q_1*Q_2)/r^2" Coulomb's law"$

$Q_{1} = - 1 C$ $Q_1=-1C$

$Q_{2} = - 2 C$ $Q_2=-2C$

$Q_{3} = 3 C$ $Q_3=3C$

$solution:$ $"solution:"$

${\to F}_{1} = k \frac{Q_{1} \cdot Q_{3}}{r^{2}}; {\to F}_{1} = k \frac{(- 1) \cdot 3}{7^{2}}; {\to F}_{1} = - \frac{3 k}{49}$ $vec F_1=k(Q_1*Q_3)/r^2" ; "vec F_1=k((-1)*3)/7^2" ; "vec F_1=-(3k)/49$

${\to F}_{2} = k \frac{Q_{2} \cdot Q_{3}}{R^{2}}; {\to F}_{2} = k \frac{(- 2) \cdot 3}{3^{2}}; {\to F}_{2} = \frac{- 6 k}{9}$ $vec F_2=k(Q_2*Q_3)/R^2" ; "vec F_2=k((-2)*3)/3^2" ; "vec F_2=(-6k)/9$

${\to F}_{2} > {\to F}_{1}$ $vec F_2 > vec F_1$

${\to F}_{R} = {\to F}_{2} - {\to F}_{1}$ $vec F_R=vec F_2- vec F_1$

${\to F}_{R} = - \frac{6 k}{9} + \frac{3 k}{49}$ $vec F_R=-(6k)/9+(3k)/49$

${\to F}_{R} = \frac{- 294 k + 27 k}{441}$ $vec F_R= (-294k+27k)/441$

${\to F}_{R} = \frac{- 267 k}{441}; {\to F}_{R} = - \frac{267 \cdot 9 \cdot 10^{9}}{441}$ $vec F_R=(-267k)/441" ; "vec F_R=-(267*9*10^9)/441$

${\to F}_{R} = - 5.45 \cdot 10^{9} N attractive force$ $vec F_R=-5.45*10^9" "N" attractive force"$

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Two charges of $- 1 C$ $-1 C$ and $- 2 C$ $-2 C$ are positioned on a line at points $- 6$ $-6$ and $4$ $4$ , respectively. What is the net force on a charge of $3 C$ $3 C$ at $1$ $1$ ?

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Two charges of −1C -1 C and −2C -2 C are positioned on a line at points −6 -6 and 4 4 , respectively. What is the net force on a charge of 3C 3 C at 1 1 ?

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Two charges of $- 1 C$ $-1 C$ and $- 2 C$ $-2 C$ are positioned on a line at points $- 6$ $-6$ and $4$ $4$ , respectively. What is the net force on a charge of $3 C$ $3 C$ at $1$ $1$ ?