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Chapter 15: Q4Q (page 616)

A rod with uniformly distributed charge 2×10-8C 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—we have to do it numerically, (5) Neither—we 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=2×10-8C

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≫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

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?

If the total charge on a thin rod of length0.4mis 2.5n/C, what is the magnitude of the electric field at a location1Cmfrom the midpoint of the rod, perpendicular to the rod?

Question: A hollow ball of radius , made of very thin glass, is rubbed all over with a silk cloth and acquires a negative charge of that is uniformly distributed all over its surface. Location A in Figure 15.64 is inside the sphere, from the surface. Location B in Figure 15.64 is outside the sphere, from the surface. There are no other charged objects nearby.


Which of the following statements about , the magnitude of the electric field due to the ball, are correct? Select all that apply. (a) At location A, is . (b) All of the charges on the surface of the sphere contribute to at location A. (c) A hydrogen atom at location A would polarize because it is close to the negative charges on the surface of the sphere. What is at location B?

What is wrong with Figure 15.35 and this associated incorrect student explanation? “The electric field at location inside the uniformly charged sphere points in the direction shown, because the charges closest to this location have the largest effect.” (Spheres provide the most common exception to the normally useful rule that the nearest charges usually make the largest contribution to the electric field.)

A plastic rod 1.7mlong is rubbed all over with wool, and acquires a charge of-2×10-8C(Figure 15.52). We choose the center of the rod to be the origin of our coordinate system, with the x axis extending to the right, the y axis extending up, and the z axis out of the page. In order to calculate the electric field at locationA=<07,0,0>, we divide the rod into eight pieces, and approximate each piece as a point charge located at the center of the piece.

(a) What is the length of one of these pieces? (b) What is the location of the center of piece number 3? (c) How much charge is on piece number? (Remember that the charge is negative.) (d) Approximating piece 3as a point charge, what is the electric field at location A due only to piece 3? (e) To get the net electric field at location A, we would need to calculatedue to each of the eight pieces, and add up these contributions. If we did that, which arrow (a–h) would best represent the direction of the net electric field at location A?
See all solutions

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