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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 chargex=L3andQ=-4q9

Step by step solution

01

Content Introduction

Suppose take +neQat distance x from the origin. The equilbrium Q must be-ne.

02

Content Explanation

Force at 0.F=0

kqQx2+kQ4qL2=0Q=-4qL2x2

Now force at P

kqQx2+kQ4q(L-x)2=0(Lx-L)=2x=L3

Substitute the value of x

Q=-4qL2+L29Q=-4q9

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Most popular questions from this chapter

Suppose there exists a third type of charge in addition to the two types we’ve called glass and plastic. Call this third type X charge. What experiment or series of experiments would you use to test whether an object has X charge? State clearly how each possible outcome of the experiments is to be interpreted.

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a. What is the electric force on a proton 2.0fmfrom the surface of the nucleus?

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Hint: Treat the spherical nucleus as a point charge

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b. How many charged particles were transferred?

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In Section 22.3we claimed that a charged object exerts a net attractive force on an electric dipole. Let’s investigate this. FIGURE CP22.77 shows a permanent electric dipole consisting of charges +q and -q separated by the fixed distance s. Charge +Q is the distance r from the center of the dipole. We’ll assume, as is usually the case in practice, that s V r.

a. Write an expression for the net force exerted on the dipole by charge +Q.

b. Is this force toward +Q or away from +Q? Explain.

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