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Chapter 23: Q25P (page 680)

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

Short Answer

Expert verified

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

Step by step solution

01

The given data

  1. Magnitude of an electric field,E=4.5脳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=位2蟺蔚0r (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:

位=2蟺蔚0rE=2蟺8.85脳10-12C2/N.m24.5脳104N/C2.0m=5.0脳10-6C/m

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

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Most popular questions from this chapter

The volume charge density of a solid nonconducting sphere of radiusR=5.60cm varies with radial distance ras given by 蚁=(14.1pC/m3)r/R. (a) What is the sphere鈥檚 total charge? What is the field magnitude E, at(b), (c) r=R/2.00, and (d) r=R? (e) Graph Eversusr.

A uniformly charged conducting sphere of1.2 mdiameter has surface charge density 8.1 mC/m2 . Find (a) the net charge on the sphere and (b) the total electric flux leaving the surface.

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

In Fig. 23-32, a butterfly net is in a uniform electric field of magnitude E=3.0mN/C. The rim, a circle of radiusa=11cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting.

The electric field at point Pjust outside the outer surface of a hollow spherical conductor of inner radius 10 cmand outer radius 20 cmhas magnitude 450 N/ Cand is directed outward. When a particle of unknown charge Qis introduced into the center of the sphere, the electric field at Pis still directed outward but is now 180 N/C.

(a) What was the net charge enclosed by the outer surface before Qwas introduced?

(b) What is charge Q?

After Qis introduced, what is the charge on the

(c) inner and

(d) outer surface of the conductor?
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