Two charges of $- 2 C$ $-2 C$ and $- 3 C$ $-3 C$ are positioned on a line at points $4$ $4$ and $- 1$ $-1$ , respectively. What is the net force on a charge of $5 C$ $5 C$ at $0$ $0$ ?

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Two charges of $- 2 C$ $-2 C$ and $- 3 C$ $-3 C$ are positioned on a line at points $4$ $4$ and $- 1$ $-1$ , respectively. What is the net force on a charge of $5 C$ $5 C$ at $0$ $0$ ?

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Answer 1 · 2017-11-07T02:42:51

$\frac{115}{8} k_{e} C^{2}$ $115/8k_eC^2$ to the negative direction.

Explanation:

Electrostatic force between two point charges can be calculated using Coulomb's law.
$F = k_{e} \frac{q_{1} \cdot q_{2}}{r^{2}}$ $F=k_e(q_1*q_2)/r^2$ , where $k_{e}$ $k_e$ is the Coulomb's constant( $k = 8.99 \cdot 10^{9} N m^{2} C^{- 2}$ $k=8.99*10^9 Nm^2C^-2$ ), $q_{1}$ $q_1$ and $q_{2}$ $q_2$ are the charges and $r$ $r$ is the distance.

Force between $- 2 C$ $-2C$ (at the point 4) and $5 C$ $5C$ (at the point 0) is
$F_{1} = k_{e} \frac{2 C \cdot 5 C}{4^{2}} = \frac{5}{8} k_{e} C^{2}$ $F_1=k_e(2C*5C)/4^2=5/8k_eC^2$ . The direction of $F_{1}$ $F_1$ is positive, for the two point charges have opposite signs.

Force between $- 3 C$ $-3C$ (at the point -1) and $5 C$ $5C$ (at the point 0) is
$F_{2} = k_{e} \frac{3 C \cdot 5 C}{1^{2}} = 15 k_{e} C^{2}$ $F_2=k_e(3C*5C)/1^2=15k_eC^2$ . This is also an attractive force, so the direction is negative.

Therefore, the net force on a charge of $5 C$ $5C$ at $0$ $0$ is $15 k_{e} C^{2} - \frac{5}{8} k_{e} C^{2} = \frac{115}{8} k_{e} C^{2}$ $15k_eC^2-5/8k_eC^2=115/8k_eC^2$ , and its direction is negative.

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Two charges of $- 2 C$ $-2 C$ and $- 3 C$ $-3 C$ are positioned on a line at points $4$ $4$ and $- 1$ $-1$ , respectively. What is the net force on a charge of $5 C$ $5 C$ at $0$ $0$ ?

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Two charges of -2 C −2C -2 C and -3 C−3C -3 C are positioned on a line at points 4 4 4 and -1 −1 -1 , respectively. What is the net force on a charge of 5 C5C 5 C at 0 0 0 ?

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Two charges of $- 2 C$ $-2 C$ and $- 3 C$ $-3 C$ are positioned on a line at points $4$ $4$ and $- 1$ $-1$ , respectively. What is the net force on a charge of $5 C$ $5 C$ at $0$ $0$ ?