Chapter 22: Q. 42 (page 625)

What is the force $\vec{F}$ on the $- 10 nC$ charge in FIGURE P $22.42$ ? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the $+ x$ -axis.

Short Answer

Expert verified

The value of force is $7.3 \times 10^{- 3} N$ and the angle is $97 . 9^{°}$ .

Step by step solution

Calculation for force on charge

Columns law of force is,

$F_{C} = F_{1 on 2} = F_{2 on 1}$

$= \frac{K |q_{1}| |q_{2}|}{r^{2}}$

Charge of one and two is,

${\vec{F}}_{12} = \frac{{Kq}_{1} q_{2}}{r^{2}} \hat{j}$

$= \frac{(9.0 \times 10^{9} N \cdot m^{2} / C^{2}) (- 10 \times 10^{- 9} C) (8 \times 10^{- 9} C)}{(0.01 m)^{2}} \hat{j}$

$= - 7.2 \times 10^{- 3} \hat{j} N$

Charge on one and three is,

$F_{13} = \frac{{Kq}_{1} q_{3}}{r_{13}^{2}}$

$= \frac{(9.0 \times 10^{9} N \cdot m^{2} / C^{2}) (- 10 \times 10^{- 9} C) (10 \times 10^{- 9} C)}{(0.03 m)^{2}}$

$= - 1 \times 10^{- 3} \hat{j} N$

Calculation of force and angle

Force for all charges is,

$F_{net} = \sqrt{{\vec{F}}_{13}^{2} + {\vec{F}}_{12}^{2}}$

$= \sqrt{{(- 1 \times 10^{- 3} N)}^{2} + {(- 7.2 \times 10^{- 3} N)}^{2}}$

$= 7.3 \times 10^{- 3} N$

Angle for negative direction is,

$α = \tan^{- 1} (\frac{(- 7.2 \times 10^{- 3} N) \hat{j}}{(- 1 \times 10^{- 3} N) \hat{i}})$

$= 82.1 °$

Angle for the positive direction is,

$α^{'} = 180 ° - α$

$= 180 ° - 82.1 °$

$= 97.9 °$

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What is the force $\vec{F}$ on the $- 10 nC$ charge in FIGURE P $22.42$ ? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the $+ x$ -axis.

Short Answer

Step by step solution

Calculation for force on charge

Calculation of force and angle

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What is the force F→on the -10nCcharge in FIGURE P22.42? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the+x-axis.

Short Answer

Step by step solution

Calculation for force on charge

Calculation of force and angle

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Physics of Motion

Modern Physics

Space Physics

Fluids

Electrostatics

Study anywhere. Anytime. Across all devices.

What is the force $\vec{F}$ on the $- 10 nC$ charge in FIGURE P $22.42$ ? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the $+ x$ -axis.