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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

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?

A proton at speed v = 3×105m/sorbits at radius r = 1.00 cmoutside a charged sphere. Find the sphere’s charge.

In Fig. 23-43, short sections of two very long parallel lines of charge are shown, fixed in place, separated by L=8.00 cmThe uniform linear charge densities are+6.0μC/mfor line 1 and-2.0μC/mfor line 2. Where along the x-axis shown is the net electric field from the two lines zero?

Charge of uniform volume densityr=1.2nC/m3fills an infinite slab between role="math" localid="1657340713406" x=-5.0cmand role="math" localid="1657340708898" x=+5.0cm.What is the magnitude of the electric field at any point with the coordinate (a) x=4.0cmand (b)x=6.0cm?

A thin-walled metal spherical shell of radius a has a charge. Concentric with it is a thin-walled metal spherical shell of radius and charge . Find the electric field at points a distance r from the common center, where

(a) r<a,

(b) a<r<b,and

(c) r>b.

(d) Discuss the criterion you would use to determine how the charges are distributed on the inner and outer surfaces of the shells.
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