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Chapter 23: Q25P (page 680)

An infinite line of charge produces a field of magnitude4.5×104N/Cat distance 2.0 m. Find the linear charge density.

Short Answer

Expert verified

The linear charge density is 5.0×10-6C/m.

Step by step solution

01

The given data

  1. Magnitude of an electric field,E=4.5×104N/C
  2. Distance of the line from the electric field,r=2.0m
02

Understanding the concept of the electric field

Using the concept of the electric field of a cylindrical Gaussian surface, we can get the required value of the linear charge density by substituting the given data.

Formula:

The electric field of a cylindrical Gaussian surface,E=λ2πε0r (1)

03

Calculation of the linear charge density

Substituting the given values in equation (1), we can get the required value of the uniform linear density on the line as follows:

λ=2πε0rE=2π8.85×10-12C2/N.m24.5×104N/C2.0m=5.0×10-6C/m

Hence, the value of the linear density is 5.0×10-6C/m.

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Most popular questions from this chapter

Figure 23-47 shows cross-sections through two large, parallel, non-conducting sheets with identical distributions of positive charge with surface charge densityσ=1.77×10-22C/m2. In unit-vector notation, what is the electric field at points (a) above the sheets, (b) between them, and (c) below them?

Two charged concentric spherical shells have radii 10.0cmand 15.0cm . The charge on the inner shell is 4.0×10-8C , and that on the outer shell is2.0×10-8C. Find the electric field (a) atr=12.0cmand (b) atr=20.0cm.

Figure 23-42 is a section of a conducting rod of radiusR1=1.30mmand lengthL=11.00m inside a thin-walled coaxial conducting cylindrical shell of radiusR2=10.0R1 and the (same) length L. The net charge on the conducting rod isQ1=+3.40×10-12; that on the shell isQ2=-2.00Q1. What are the (a) magnitude Eand (b) direction (radially inward or outward) of the electric field at radial distancer=2.00R2? What are (c) Eand (d) the direction atr=5.00R1? What is the charge on the (e) interior and (f) exterior surface of the shell?

A charge of 6.00 pCis spread uniformly throughout the volume of a sphere of radius r = 4.00 cm. What is the magnitude of the electric field at a radial distance of

(a) 6.00 cmand

(b) 3.00 cm?

Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an x-axis through the sheets. The scale of the vertical axis is set byEs=6.0×105N/C. What is the ratio of the charge density on sheet 3 to that on sheet 2?
See all solutions

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