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Chapter 23: Q4P (page 679)

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.

Short Answer

Expert verified

The electric flux through the netting is -1.1×10-4N.m2/C.

Step by step solution

01

The given data

  1. The magnitude of the electric field,E=3.0m.N/C
  2. Radius of the circle,a=11cm1m100cm=0.11m
  3. The net contains no charge.
02

Understanding the concept of electric flux

Using the concept of Gauss flux theorem through an enclosed surface, we can get the flux value of the electric field through a circular surface.

Formula:

The electric flux through a circular surface, ϕ=πa2E (1)

03

Calculation of the electric flux

The flux through the flat surface encircled by the rim is given using equation (1) and thus, the flux through the netting is given as:

ϕ'=-ϕ=-π(0.11m)2(3.0×10-3N/C)=-1.1×10-4N.m2/C

Hence, the value of the flux is -1.1×10-4N.m2/C.

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Most popular questions from this chapter

Figure 23-34 shows a closed Gaussian surface in the shape of a cube of edge length 2.00 m. It lies in a region where the non-uniform electric field is given by E→=[(3.00x+4.00)i^+6.00j^+7.00k^]N/C, with xin meters. What is the net charge contained by the cube?

Flux and non-conducting shells. A charged particle is suspended at the center of two concentric spherical shells that are very thin and made of non-conducting material. Figure 23-37a shows a cross section. Figure 23-37b gives the net flux ϕ through a Gaussian sphere centered on the particle, as a function of the radius r of the sphere. The scale of the vertical axis is set by ϕ=5.0×105Nm2/C. (a) What is the charge of the central particle? What are the net charges of (b) shell A and (c) shell B?

A Gaussian surface in the form of a hemisphere of radiusR=5.68cmlies in a uniform electric field of magnitudeE=2.50 N/C. The surface encloses no net charge. At the (flat) base of the surface, the field is perpendicular to the surface and directed into the surface. What is the flux through

(a) the base and

(b) the curved portion of the surface?

In Fig. 23-49, a small, non-conducting ball of massm=1.0mgand charge q=2.0×10-8C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ=30owith a vertical, uniformly charged non-conducting sheet (shown in cross-section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density s of the sheet.

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