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Chapter 15: Q13Q (page 616)

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.

Short Answer

Expert verified

The electric field at locations near the center of a uniformly charged disk does not vary with distance because with respect to these points the disk behaves like an infinite charged sheet.

Step by step solution

01

Identification of given data

A uniformly charged disk.

02

Field due to an infinite uniformly charged sheet

The electric field due to an infinitely long uniformly charged disk is constant and does not vary with distance from the sheet.

03

Determination of the variation of electric field near the centre of a uniformly charged disk

For points very close to the centre of a uniformly charged disk, the distance of the points from the disk are negligible compared to the dimension of the disk. Hence with respect to these points, the disk behaves like an infinite sheet, the field due to which is constant. Thus, the electric field measured at such points do not vary much with distance from the disk.

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Most popular questions from this chapter

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?

A capacitor consists of two large metal disks of radius 1.1 m placed parallel to each other, a distance of 1.2 mm apart. The capacitor is charged up to have an increasing amount of charge +Q on one disk and −Q on the other. At about what value of Q does a spark appear between the disks?

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=Qε0Lx1/2

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

Suppose that the radius of a disk is 21 cm, and the total charge distributed uniformly all over the disk is 5×10-6C. (a) Use the exact result to calculate the electric field 1 mm from the center of the disk. (b) Use the exact result to calculate the electric field 3 mm from the center of the disk. (c) Does the field decrease significantly?

For a disk of radius R=20cm and Q=6×10-6C, calculate the electric field 2 mm from the center of the disk using all three equations:

role="math" localid="1656928965291" E=(Q/A)2ε0[1-z(R2+z)1/2]

E≈Q/A2e0[1-zR],andE≈Q/A2e0

How good are the approximate equations at this distance? For the same disk, calculate E at a distance of 5 cm (50 mm) using all three equations. How good are the approximate equations at this distance?
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