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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

Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

Two 1.0 kg masses are 1.0 m apart (center to center) on a frictionless table. Each has +10 mC of charge.

a. What is the magnitude of the electric force on one of the masses?

b. What is the initial acceleration of this mass if it is released and allowed to move?

What is the force $\overset{鈫�}{F}$ on the $1.0 nC$ charge at the bottom in FIGURE $P 22.45$ $?$ Give your answer in component form.

FIGURE $P 22.51$ shows four charges at the corners of a square of side $L$ . What is the magnitude of the net force on $q$ ?

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?

See all solutions

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