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Chapter 22: Q. 24 (page 625)

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?

Short Answer

Expert verified

The magnitude, sign and x-coordinate of the third charge $x = \frac{L}{3} a n d Q = - \frac{4 q}{9}$

Step by step solution

01

Content Introduction

Suppose take $+ n e Q$ at distance x from the origin. The equilbrium Q must be $- n e$ .

02

Content Explanation

Force at $0 .$ $F = 0$

$k \frac{q Q}{x^{2}} + k \frac{Q 4 q}{L^{2}} = 0 Q = - \frac{4 q}{L^{2}} x^{2}$

Now force at P

$k \frac{q Q}{x^{2}} + k \frac{Q 4 q}{{(L - x)}^{2}} = 0 (\frac{L}{x} - L) = 2 x = \frac{L}{3}$

Substitute the value of x

$Q = - \frac{4 q}{L^{2}} + \frac{L^{2}}{9} Q = - \frac{4 q}{9}$

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Most popular questions from this chapter

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.

Object A, which has been charged to +4.0 nC, is at the origin. Object B, which has been charged to -8.0 nC, is at 1x, y2 = 10.0 cm, 2.0 cm2. Determine the electric force on each object. Write each force vector in component form

What is the net electric force on charge B in FIGURE?

What is the force $\vec{F}$ on the $1.0 n C$ charge in Figure ? Give your answer as a magnitude and a direction.

The net force on the $1.0 nC$ charge in FIGURE $P 22.48$ is zero What is $q$ $?$

See all solutions

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