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Chapter 23: Q58P (page 683)

A uniform surface charge of density 8.0nC/m2is distributed over the entire x-yplane. What is the electric flux through a spherical Gaussian surface centered on the origin and having a radius of5.0cm ?

Short Answer

Expert verified

The electric flux through a spherical Gaussian surface centered on the origin and having a radius of 5.0 cm is 7.1Nm2/C.

Step by step solution

01

Listing the given quantities

surface charge of density8.0nc/m2

the radius of the Gaussian surface is 5.0 cm

02

Understanding the concept of Gauss Law

Using the statement of Gauss law determine the electric flux through the spherical gauss an surface centered on the origin and having a radius of 5.0 cm

Gauss Law

Formula:

蠒=qenc蔚0

03

Explanation

From Gauss鈥檚 law, we have

蠒=qenc蔚0=蟽蟺谤2蔚0=8.0脳10-9C/m3蟺(0.050m)2(8.85脳10-12C2/N.m2)=7.1Nm2/C

Electric flux through a spherical Gaussian surface centered on the origin and having a radius of 5.0 cm is 7.1N.m2/C

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Most popular questions from this chapter

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?

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?

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

Chargeis uniformly distributed in a sphere of radius R.

(a) What fraction of the charge is contained within the radius is r = R/2.00?

(b) What is the ratio of the electric field magnitude at r=R/2.00to that on the surface of the sphere?

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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