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Chapter 23: Q68P (page 684)

The net electric flux through each face of a die (singular of dice) has a magnitude in units of 103Nm2/Cthat is exactly equal to the number of spots Non the face (1 through 6). The flux is inward for Nodd and outward for Neven. What is the net charge inside the die?

Short Answer

Expert verified

The net charge inside the die is2.66×10-8C .

Step by step solution

01

Listing the given quantities

  • The net electric flux =103N.m2/C
02

Understanding the concept of Gauss law

Gauss law describes the relation between charge and electric field in a static situation. The equation for Gauss law is,

ε0Φ=qenc

Here, qencis the net charge inside an imaginary closed surface and is the net flux of the electric field through the surface.

03

Net charge inside the die

Let ∅0=103N.m2/C.

The net flux through the entire surface of the dice is given by:

∅=∑n-16Φn=∑n-16(-1)nnϕ0=ϕ0(-1+2-3+4-5+6)=3ϕ0

Thus, the net charge enclosed is:

role="math" localid="1657360360230" q=ε0ϕ=3ε0ϕ0=38.85×10-12C2/N.m2103N.m2/C=2.66×10-8C

Therefore, the net charge inside the die is=2.66×10-8C .

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Most popular questions from this chapter

Figure 23-50 shows a very large non-conducting sheet that has a uniform surface charge density of σ=-2.00μC/m2, it also shows a particle of chargeQ=6.00μC, at distance dfrom the sheet. Both are fixed in place. If d=0.200m , at what (a) positive and (b) negative coordinate on the xaxis (other than infinity) is the net electric field Enet of the sheet and particle zero? (c) If d=0.800m , at what coordinate on the x-axis isEnet=0?

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

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?

The electric field in a particular space isE→=(x+2)i^N/C, with xin meters. Consider a cylindrical Gaussian surface of radius that is coaxial with the x-axis. One end of the cylinder is atx=0 . (a) What is the magnitude of the electric flux through the other end of the cylinder at X=2.0m? (b) What net charge is enclosed within the cylinder?
See all solutions

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