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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

Two long, charged, thin-walled, concentric cylindrical shells have radii of3.0 cm and 6.0 cm . The charge per unit length is 5.0×10-6C/mon the inner shell and -7.0×10-6C/mon the outer shell. What are the (a) magnitude Eand (b) direction (radially inward or outward) of the electric field at radial distance r=4.0 cm ? What are (c) Eand (d) the direction at r=8.0 cm?

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.

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?

Assume that a ball of charged particles has a uniformly distributed negative charge density except for a narrow radial tunnel through its center, from the surface on one side to the surface on the opposite side. Also assume that we can position a proton anywhere along the tunnel or outside the ball. Let Fr be the magnitude of the electrostatic force on the proton when it is located at the ball’s surface, at radius R. As a multiple of R, how far from the surface is there a point where the force magnitude is if we move the proton (a) away from the ball and (b) into the tunnel?

Equation 23-11 (E=σ/ε0) gives the electric field at points near a charged conducting surface. Apply this equation to a conducting sphere of radius rand charge q, and show that the electric field outside the sphere is the same as the field of a charged particle located at the center of the sphere.

See all solutions

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