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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=14蟺蔚0Qrr2+(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

Question: Breakdown field strength for air is roughly . If the electric field is greater than this value, the air becomes a conductor. (a) There is a limit to the amount of charge that you can put on a metal sphere in air. If you slightly exceed this limit, why would breakdown occur, and why would the breakdown occur very near the surface of the sphere, rather than somewhere else? (b) How much excess charge can you put on a metal sphere of radius without causing breakdown in the neighboring air, which would discharge the sphere? (c) How much excess charge can you put on a metal sphere of onlyradius? These results hint at the reason why a highly charged piece of metal tends to spark at places where the radius of curvature is small, or at places where there are sharp points.

Suppose that the radius of a disk is R=20, and the total charge distributed uniformly all over the disk isrole="math" localid="1656058758873" Q=6脳10-6C. Use the exact result to calculate the electric fieldfrom the center of the disk, and alsofrom the center of the disk. Does the field decrease significantly?

A student claimed that the equation for the electric field outside a cube of edge length L, carrying a uniformly distributed charge Q, at a distancex from the center of the cube, was

role="math" localid="1668495301957" E=Q蔚0Lx1/2

Explain how you know that this cannot be the right equation.

A disk of radius 16 cm has a total charge 4 脳 10鈭�6 C distributed uniformly all over the disk. (a) Using the exact equation, what is the electric field 1 mm from the center of the disk? (b) Using the same exact equation, find the electric field 3 mm from the center of the disk. (c) What is the percent difference between these two numbers?

A rod is 2.5m long. Its charge is -2脳10-7C. The observation location is 4cm from the rod, in the mid plane. In the expression

E=14蟺蔚0Qrr2+(L2)2

what isr in meters?
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