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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

For a disk of radius 20 cm with uniformly distributed charge 7×10-6C, calculate the magnitude of the electric field on the axis of the disk, 5 mm from the center of the disk, using each of the following equations:

(a)E=(Q/A)2ε0[1-zR2+z21/2]

(b)E≈Q/A2ε0[1-zR]

(c)E≈Q/A2ε0

(d) How good are the approximate equations at this distance? (e) At what distance does the least accurate approximation for the electric field give a result that is closest to the most accurate: at a distance R/2, close to the disk, at a distance R, or far from the disk?

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?

Consider setting up an integral to find an algebraic expression for the electric field of a uniformly charged rod of length L , at a location on the midplane. If we choose an origin at the center of the rod, what are the limits of integration?

Define “fringe field.”

A thin plastic spherical shell of radius 5 cmhas a uniformly distributed charge of -25nCon its outer surface. A concentric thin plastic spherical shell of radius 8 cmhas a uniformly distributed charge of+64nC on its outer surface. Find the magnitude and direction of the electric field at distances of, 3 cm, 7 cm and 10 cmfrom the center. See Figure 15.63.
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