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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

A strip of invisible tape 0.12 mlong by 0.013 mwide is charged uniformly with a total net charge of 3nC(nano =1×10-9) and is suspended horizontally, so it lies along the xaxis, with its center at the origin, as shown in Figure 15.55. Calculate the approximate electric field at location<0,0.03,0>m(location A) due to the strip of tape. Do this by dividing the strip into three equal sections, as shown in Figure 15.55, and approximating each section as a point charge.

(a) What is the approximate electric field at Adue to piece 1? (b) What is the approximate electric field at Adue to piece 2? (c) What is the approximate electric field at Adue to piece 3? (d) What is the approximate net electric field at A? (e) What could you do to improve the accuracy of your calculation?

A disk of radius 16 cm has a total charge 4 × 10−6 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?

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 ∆Qis the charge on one piece of the ring. ∆θis the angle subtended by one piece of the ring (or, alternatively, ∆ris the arc length of one piece). What is∆Q, expressed in terms of given constants and an integration variable? What are the integration limits?

If the magnitude of the electric field in air exceeds roughly3×106N3, the air break down and a spark forms. For a two-disk capacitor of radius 51 cm with a gap of 2 mm, if the electric field inside is just high enough that a spark occurs, what is the strength of the fringe field just outside the center of the capacitor?

A thin plastic spherical shell of radius 5 cmhas a uniformly distributed charge of -25nCon its outer surface. A concentric thin plastic spherical shell of radius 8 cmhas a uniformly distributed charge of+64nC on its outer surface. Find the magnitude and direction of the electric field at distances of, 3 cm, 7 cm and 10 cmfrom the center. See Figure 15.63.
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