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Chapter 15: Q3Q (page 616)

Graph the magnitude of the full expression for the field E of a rod along the midplane vs. r. Does Efall off monotonically(with distance)?

Short Answer

Expert verified

The plot of Evs r is

Efalls off monotonically with distance.

Step by step solution

01

Given data

A uniformly charged rod of length with an electric field is being measured at a distancer from it along the midplane.

02

Electric field due to a uniformly charged rod

The electric field due to a rod of lengthLand charge Quniformly distributed at a distancer from it on its mid plane is,

role="math" localid="1668497036664" E=14πε0Qrr2+(L2)2.....(i)
03

Step 3:Determination of the plot of the electric field

Plot the electric field defined in equation (i) as a function of ras follows:

As can be seen from the plot, the electric field falls of monotonically with distance.

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Most popular questions from this chapter

A thin-walled hollow circular glass tube, open at both ends, has a radius R and length L. The axis of the tube lies along the x axis, with the left end at the origin (Figure 15.58). The outer sides are rubbed with silk and acquire a net positive charge Q distributed uniformly. Determine the electric field at a location on the x axis, a distance w from the origin. Carry out all steps, including checking your result. Explain each step. (You may have to refer to a table of integrals.)

Consider a thin plastic rod bent into a semicircular arc of radius Rwith center at the origin (Figure 15.57). The rod carries a uniformly distributed negative charge -Q.

(a) Determine the electric field E→at the origin contributed by the rod. Include carefully labeled diagrams, and be sure to check your result. (b) An ion with charge -2eand mass is placed at rest at the origin. After a very short time ∆tthe ion has moved only a very short distance but has acquired some momentum .P→Calculate P→.

A plastic rod 1.7mlong is rubbed all over with wool, and acquires a charge of-2×10-8C(Figure 15.52). We choose the center of the rod to be the origin of our coordinate system, with the x axis extending to the right, the y axis extending up, and the z axis out of the page. In order to calculate the electric field at locationA=<07,0,0>, we divide the rod into eight pieces, and approximate each piece as a point charge located at the center of the piece.

(a) What is the length of one of these pieces? (b) What is the location of the center of piece number 3? (c) How much charge is on piece number? (Remember that the charge is negative.) (d) Approximating piece 3as a point charge, what is the electric field at location A due only to piece 3? (e) To get the net electric field at location A, we would need to calculatedue to each of the eight pieces, and add up these contributions. If we did that, which arrow (a–h) would best represent the direction of the net electric field at location A?

Two rings of radius 4 cm are 12 cm apart and concentric with a common horizontal x axis. The ring on the left carries a uniformly distributed charge of +40nC, and the ring on the right carries a uniformly distributed charge of -40nC. (a) What is theelectric field due to the right ring at a location midway between the two rings? (b) What is the electric field due to the left ring at a location midway between the two rings? (c) What is the net electric field at a location midway between the two rings? (d) If a charge of -2nCwere placed midway between the rings, what would be the force exerted on this charge by the rings?

Explain qualitatively how it is possible for the electric field at locations near the center of a uniformly charged disk not to vary with distance away from the disk.
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