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

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

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Answer 1 · 2017-05-21T01:59:56

The forces on the $3$ $3$ $C$ $C$ charge due to each of the other charges can simply be added together.

The net force is $F = \frac{k \times 2 \times 3}{6^{2}} + \frac{k \times 4 \times 3}{3^{2}} = 1.35 \times 10^{10}$ $F = (kxx2xx3)/6^2+(kxx4xx3)/3^2 = 1.35 xx 10^10$ $C$ $C$

Explanation:

The charges in question are all positive, so the forces will be repulsive. The $3$ $3$ $C$ $C$ charge will be experiencing a force to the right, if we imagine the number line.

The distance from the $2$ $2$ $C$ $C$ charge to the $3$ $3$ $C$ $C$ charge is $6$ $6$ $m$ $m$ (we are not told the units of distance being used, but metres are the appropriate SI unit). The distance from the $4$ $4$ $C$ $C$ charge to the $3$ $3$ $C$ $C$ charge is $3$ $3$ $m$ $m$ .

The net force, then, is:

$F = \frac{k \times 2 \times 3}{6^{2}} + \frac{k \times 4 \times 3}{3^{2}}$ $F = (kxx2xx3)/6^2+(kxx4xx3)/3^2$

where $k = 9 \times 10^{9}$ $k = 9xx10^9$ $N m^{2} C^{- 2}$ $Nm^2C^-2$

$F = \frac{k \times 2 \times 3}{6^{2}} + \frac{k \times 4 \times 3}{3^{2}} = 1.35 \times 10^{10}$ $F = (kxx2xx3)/6^2+(kxx4xx3)/3^2 = 1.35 xx 10^10$ $C$ $C$

This is a very large force, but these are very large charges, quite close together, and the constant is large.

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

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Explanation:

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

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Explanation:

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