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Chapter 22: Q. 49 (page 626)

Charge $q_{2}$ in FIGURE $P 22.49$ is in equilibrium. What is $q_{1}$ $?$

Short Answer

Expert verified

Charge is $- 20 nC$ .

Step by step solution

01

Calculation for force on charge

Two charged particles, one with a charge of $q_{1}$ .

And the other with a charge of $q_{2}$ , separated by a distance of $r$ .

The two particles exert forces on each other, with the force decreasing as the distance between them grows and increasing as the size of the charges increases.

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

Force for charge $q_{3}$ and $q_{2}$ :

${\overset{鈫�}{F}}_{32} = \frac{{Kq}_{3} q_{2}}{r_{32}^{2}}$

$= \frac{(9.0 脳 10^{9} N 路 m^{2} / C^{2}) (5 脳 10^{- 9} C) q_{2}}{(0.1 m)^{2}}$

$= 4500 q_{2}$

02

Calculation of charge

Force for charge $q_{1}$ and $q_{2}$

${\overset{鈫�}{F}}_{12} = \frac{{Kq}_{1} q_{2}}{r_{12}^{2}}$

$= \frac{(9.0 脳 10^{9} N 路 m^{2} / C^{2}) q_{1} q_{2}}{(0.2 m)^{2}}$

$= 225 脳 10^{9} q_{1} q_{2}$

{\overset{鈫�}{F}}_{12} = - {\overset{鈫�}{F}}_{32}

so,

${\overset{鈫�}{F}}_{12} = - {\overset{鈫�}{F}}_{32}$

$225 脳 10^{9} q_{1} q_{2} = - 4500 q_{2}$

$q_{1} = - \frac{4500}{225 脳 10^{9}}$

$q_{1} = - 20 脳 10^{- 9} C$

$q_{1} = - 20 nC$

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Most popular questions from this chapter

What are the electric fields at points 1, 2, and 3 in FIGURE P22.64? Give your answer in component form.

Two positive point charges q and 4q are at x = 0 and x = L, respectively, and free to move. A third charge is placed so that the entire three-charge system is in static equilibrium. What are the magnitude, sign, and x-coordinate of the third charge?

A glass rod is charged to +8.0 nC by rubbing.

a. Have electrons been removed from the rod or protons added?

b. How many electrons have been removed or protons added?

A $2.0 g$ metal cube and a $4.0 g$ metal cube are $6.0 cm$ apart, measured between their centers, on a horizontal surface. For both, the coefficient of static friction is $0.65$ . Both cubes, initially neutral, are charged at a rate of $7.0 nC / s$ . How long after charging begins does one cube begin to slide away? Which cube moves first?

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.

See all solutions

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