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Chapter 15: Q4Q (page 616)

A rod with uniformly distributed charge 2脳10-8C is 50cm long. We need to calculate E at a distance of 1cm from the midpoint of the rod. Which equation for the electric field of a rod should we use? (1) Exact, (2) Approximate, (3) Either exact or approximate, (4) Neither鈥攚e have to do it numerically, (5) Neither鈥攚e need to integrate.

Short Answer

Expert verified

The approximate equation can be used.

Step by step solution

01

Identification of given data

The charge on the rod is q=2脳10-8C

The length of the rod is L=50cm

The distance of the measurement point from the rod is r=1cm

02

Approximation of electric field due to a charged rod

The approximated form of the electric field due to a charged rod on its mid plane is used when the distance of the point where the field is to be obtained from the rod is negligible compared to the length of the rod.

03

Determination of the method to obtain the field

Since the length of the rod L=50cm is much greater than the distance of the measurement point r=1cm , that is

L鈮�r

the approximate form of the electric field formula can be safely used.

Hence, the approximate equation can be used.

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Most popular questions from this chapter

In Figure 15.61 are two uniformly charged disks of radius R that are very close to each other (gap鈮猂). The disk on the left has a charge of鈭�Qleftand the disk on the right has a charge of +Qright(Qrightis greater thanQleft). A uniformly charged thin rod of length L lies at the edge of the disks, parallel to the axis of the disks and cantered on the gap. The rod has a charge of +Qrod.

(a) Calculate the magnitude and direction of the electric field at the point marked 脳 at the center of the gap region, and explain briefly, including showing the electric field on a diagram. Your results must not contain any symbols other than the given quantities R,Qleft, Qright, L, andQrod(and fundamental constants), unless you define intermediate results in terms of the given quantities. (b) If an electron is placed at the center of the gap region, what are the magnitude and direction of the electric force that acts on the electron?

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.

Consider the algebraic expression for the electric field of a uniformly charged ring, at a location on the axis of the ring. Q is the charge on the entire ring, and 鈭�Qis the charge on one piece of the ring. 鈭�胃is the angle subtended by one piece of the ring (or, alternatively, 鈭�ris the arc length of one piece). What is鈭�Q, expressed in terms of given constants and an integration variable? What are the integration limits?

Consider a thin glass rod of length L lying along the x axis with one end at the origin. The rod carries a uniformly distributed positive charge Q.

At a location d > L, on the x axis to the right of the rod in Figure 15.56, what is the electric field due to the rod? Follow the standard four steps. (a) Use a diagram to explain how you will cut up the charged rod, and draw the contributed by a representative piece. (b) Express algebraically the contribution each piece makes to the electric field. Be sure to show your integration variable and its origin on your drawing. (c) Write the summation as an integral, and simplify the integral as much as possible. State explicitly the range of your integration variable. Evaluate the integral. (d) Show that your result is reasonable. Apply as many tests as you can think of

Define 鈥渇ringe field.鈥�
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