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Chapter 23: Q7P (page 679)

A particle of charge 1.8μCis at the center of a Gaussian cube55cmon edge. What is the net electric flux through the surface?

Short Answer

Expert verified

The net electric flux through the surface is 2.0×105N.m2/C.

Step by step solution

01

The given data

  1. Charge of the particle,q=1.8μC
  2. Edge length of cube,a=55cm1m100cm=0.55m
02

Understanding the concept of Gauss law-planar symmetry

Using the concept of Gauss law and the planar symmetry, we can get the required values of the electric field at the left of the plates, right of the plates, and between the plates.

Formula:

The total flux through any surface, ϕ=qε0 (1)

03

Calculation of the net flux through any cube surface

As the cube has six surfaces, thus, the net flux through each surface of the cube is given using equation (1) such that,

ϕ=1.8×10-6C6×8.85×10-12C2/N.m2=2.0×105N.m2/C

Hence, the value of the required flux is2.0×105N.m2/C

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Most popular questions from this chapter

Figure 23-23 shows, in cross section, a central metal ball, two spherical metal shells, and three spherical Gaussian surfaces of radii R, 2R, and 3R, all with the same center. The uniform charges on the three objects are: ball, Q; smaller shell, 3Q; larger shell, 5Q. Rank the Gaussian surfaces according to the magnitude of the electric field at any point on the surface, greatest first.

Figure 23-41ashows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are non-conducting and thin and have uniform surface charge densities on their outer surfaces. Figure 23-41bgives the radial component Eof the electric field versus radial distance rfrom the common axis, and. What is the shell’s linear charge density?

A particle of charge+q is placed at one corner of a Gaussian cube. What multiple ofq/ε0gives the flux through (a) each cube face forming that corner and (b) each of the other cubes faces?

Figure 23-29 shows four Gaussian surfaces consisting of identical cylindrical midsections but different end caps. The surfaces are in a uniform electric fieldE→that is directed parallel to the central axis of each cylindrical midsection. The end caps have these shapes:S1, convex hemispheres;S3, concave hemispheres;S3, cones;S4, flat disks. Rank the surfaces according to (a) the net electric flux through them and (b) the electric flux through the top end caps, greatest first.

What mass of water fell on the town in Problem 7? Water has a density of1.0×103×kg/m3.
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