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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

A thin glass rod of length 80 cmis rubbed all over with wool and acquires a charge of 60 nC, distributed uniformly over its surface. Calculate the magnitude of the electric field due to the rod at a location 7 cmfrom the midpoint of the rod. Do the calculation two ways, first using the exact equation for a rod of any length, and second using the approximate equation for a long rod.

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?

Consider a capacitor made of two rectangular metal plates of length L and width W, with a very small gap s between the plates. There is a charge +Qon one plate and a charge 鈭扱on the other. Assume that the electric field is nearly uniform throughout the gap region and negligibly small outside. Calculate the attractive force that one plate exerts on the other. Remember that one of the plates doesn鈥檛 exert a net force on itself

Define 鈥渇ringe field.鈥�

A clear plastic pen 12 cmlong is rubbed all over with wool, and acquires a negative charge of -2nC. You want to figure out the electric field a distance of 18 mmfrom the pen, near the middle of the pen. (a) You decide to model the pen as a rod consisting of a series of five segments, each of which you will consider to be approximately point-like. What is the length of each segment in meters? (b) What is the amount of charge 鈭�Qon each of the five segments? (c) In general, if the rod has a length Land total charge Q, and you divide the rod into Nsegments, what is the amount of charge鈭�Qon each piece? (d) If the length of each segment is dL, write a symbolic expression for the number of pieces Nin terms of the length of the rod Land the length of one piece dL.(e) Now write a symbolic expression for the amount of charge on each piece in terms of the length of the rod and the length of a small piece.
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