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Chapter 24: Q18P (page 711)

Two charged particles are shown in Fig. 24-39a. Particle 1, with charge q1, is fixed in place at distance d. Particle 2, with charge q2, can be moved along the xaxis. Figure 24-39bgives the net electric potential Vat the origin due to the two particles as a function of the xcoordinate of particle 2. The scale of the xaxis is set by xs = 16.0 cm. The plot has an asymptote of V = 5.76 x 10-7 Vas x→∞What is q2in terms of e?

Short Answer

Expert verified

The charge on q2 is -32e.

Step by step solution

01

Given

Charge q1 is fixed in a place at a distance d.

charge q2 can move along x-axis.

02

Understanding the concept

When the charge q2 is infinitely far away, the potential at the origin is due only to q1. This means the asymptote represents the potential due to the charge q1 .

V1=q14πε0d

03

Calculate q2 in terms of e

The asymptote represents the potential due to the charge q1. Therefore-

5.76×10-7V=q14πε0dq1d=6.41×10-17C/m

If the charge q2 is located at x = 0.08 m, the net potential vanishes

V1+V2=0kq20.08m+kq1d=0q2=-q1d0.08m=-5.13×10-18C=-5.13×10-18C1.6×10-19C/1e=-32e

Interms of e the charge on q2 is -32e.

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Most popular questions from this chapter

Question: In Fig. 24-53, seven charged particles are fixed in place to form a square with an edge length of 4.0 cm. How much work must we do to bring a particle of charge +6Einitially at rest from an infinite distance to the center of the square?

(a) Using Eq. 24-32, show that the electric potential at a point on the central axis of a thin ring (of charge q and radius R ) and at distance Z from the ring is,V=14πεo⋅qR2+z2

(b) From this result, derive an expression for the electric field magnitude

E at points on the ring’s axis; compare your result with the calculation of E in Module 22-4.

Proton in a well.Figure 24-59shows electric potential Valong an xaxis.The scale of the vertical axis is set by Vs=10.0 V. A proton is to be released at x=3.5 cmwith initial kinetic energy 4.00 eV. (a) If it is initially moving in the negativedirection of the axis, does it reach a turning point (if so, what is the x-coordinate of that point) or does it escape from the plottedregion (if so, what is its speed at x=0)? (b) If it is initially movingin the positive direction of the axis, does it reach a turning point (ifso, what is the xcoordinate of that point) or does it escape from theplotted region (if so, what is its speed at x=6.0 cm)? What are the (c) magnitude Fand (d) direction (positive or negative direction ofthe xaxis) of the electric force on the proton if the proton movesjust to the left of x=3.0 cm? What is (e) Fand (f) the direction ifthe proton moves just to the right of x=5.0 cm?

Three particles, charge q1=+10μC, q2=-20μC , and q3=+μC , are positioned at the vertices of an isosceles triangle as shown in Fig. 24-62. If a=10cm and b=6.0cm , how much work must an external agent do to exchange the positions of (a) q1 and q3 and, instead, (b) q1 andq2?

Figure 24-29 shows four arrangements of charged particles, all the same distance from the origin. Rank the situations according to the net electric potential at the origin, most positive first. Take the potential to be zero at infinity.
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