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Chapter 22: Q. 43 (page 625)

What is the force $\overset{鈫�}{F}$ 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 $20.2 脳 10^{- 5} N$ and the angle is $45^{掳}$ .

Step by step solution

01

Force for y-axis

Force is,

$F_{y} = \frac{1}{4 {蟺系}_{o}} 脳 \frac{q_{1} q_{3}}{r^{2}} 蝉颈苍胃$

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

$F_{y} = 14.4 脳 10^{- 5} N (- j)$

02

Calculation for force on x axis

Force is,

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

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

$F_{x} = 14.2 脳 10^{- 5} N (i)$

03

Figure for force in all axis

04

Calculation of overall force

Force is,

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

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

$F_{net} = 20.2 脳 10^{- 5} N$

Angle is,

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

$= - 45 掳$

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Most popular questions from this chapter

Charges A and B in FIGURE Q22.14 are equal. Each charge exerts a force on the other of magnitude F. Suppose the charge of B is increased by a factor of 4, but everything else is unchanged. In terms of F,

(a) what is the magnitude of the force on A, and

(b) what is the magnitude of the force on B?

What are the electric fields at points 1, 2, and 3 in FIGURE P22.63? Give your answer in component form.

44. What is the force $\overset{鈫�}{F}$ on the $- 1.0 n C$ charge in the middle of FIGURE P $22.44$ due to the four other charges? Give your answer in component form.

Two $1.0 g$ spheres are charged equally and placed $2.0 c m$ apart. When released, they begin to accelerate at role="math" localid="1650358356011" $150 m / s^{2}$ . What is the magnitude of the charge on each sphere?

Four lightweight balls $A, B, C, a n d D$ are suspended by threads. Ball $A$ has been touched by a plastic rod that was rubbed with wool. When the balls are brought close together, without touching, the following observations are made:

鈥� Balls $B, C, a n d D$ are attracted to ball $A .$

鈥� Balls $B a n d D$ have no effect on each other.

鈥� Ball $B$ is attracted to ball $C .$

What are the charge states (glass, plastic, or neutral) of balls $A, B, C, a n d D$ ? Explain.

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