Chapter 22: Q. 43 (page 625)

What is the force $\vec{F}$ on the $5.0 nC$ charge in FIGURE P $22.43$ ? 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 $20.2 \times 10^{- 5} N$ and the angle is $45^{°}$ .

Step by step solution

Force for y-axis

Force is,

$F_{y} = \frac{1}{4 {πϵ}_{o}} \times \frac{q_{1} q_{3}}{r^{2}} sinθ$

$= 9 \times 10^{9} \times \frac{(10 \times 10^{- 9} C) (5 \times 10^{- 9} C)}{{(5 \times 10^{- 2} m)}^{2}} \times \frac{4}{5}$

$F_{y} = 14.4 \times 10^{- 5} N (- j)$

Calculation for force on x axis

Force is,

$F_{x} = \frac{1}{4 {πϵ}_{o}} [\frac{q_{2} q_{3}}{{(r_{32})}^{2}} - \frac{q_{1} q_{3}}{{(r_{13})}^{2}} cosθ]$

$= 9 \times 10^{9} \times [\frac{(5) nc (5) nc}{9 cm} - \frac{3}{5} \times \frac{(10) nc (5) nc}{25 cm}] \times \frac{10^{- 18}}{10^{- 4}}$

$F_{x} = 14.2 \times 10^{- 5} N (i)$

Figure for force in all axis

Calculation of overall force

Force is,

$F_{net} = \sqrt{F_{x}^{2} + F_{y}^{2}}$

$= \sqrt{(14.2 N)^{2} + (14.4 N)^{2}} \times 10^{- 5}$

$F_{net} = 20.2 \times 10^{- 5} N$

Angle is,

$θ = \tan^{- 1} (\frac{- 14.4 N}{14.2 N} \times \frac{10^{- 3}}{10^{- 3}})$

$= - 45 °$

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What is the force $\vec{F}$ on the $5.0 nC$ charge in FIGURE P $22.43$ ? 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

Force for y-axis

Calculation for force on x axis

Figure for force in all axis

Calculation of overall force

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What is the force F→on the 5.0nCcharge in FIGURE P22.43? 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

Force for y-axis

Calculation for force on x axis

Figure for force in all axis

Calculation of overall force

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Rotational Dynamics

Nuclear Physics

Further Mechanics and Thermal Physics

Physics of Motion

Oscillations

Fluids

Study anywhere. Anytime. Across all devices.

What is the force $\vec{F}$ on the $5.0 nC$ charge in FIGURE P $22.43$ ? Give your answer as a magnitude and an angle measured cw or ccw (specify which) from the $x$ -axis.