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Chapter 23: Q66P (page 683)

A charged particle causes an electric flux of -750 N.m2/Cto pass through a spherical Gaussian surface of 10.0 cmradius centered on the charge.

(a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

(b) What is the charge of the particle?

Short Answer

Expert verified

a) If the radius of the Gaussian surface were doubled, the amount of flux passing through the surface is-750N.m2/C .

b) Charge on the particle is -6.64×109C.

Step by step solution

01

Listing the given quantities

  • The electric flux =-750N.m2/C
  • Gaussian surface radius = 10.0 cm
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,

ε0∅=qenc

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

03

(a) Calculation of the flux passing through the surface

By doubling the area, the only surface has increased. It does not change the amount of charge enclosed by the surface area. From the equation,

ε0Φ=qenc

We can see that flux depends on the enclosed charge. Therefore, the flux will remain the same as-750N.m2/C .

04

(b) Calculation of the charge on the particle

We use ϕ=q/ε0to calculate the charge as:

q=∅ε0=8.85×10-12C2/N.m2-750N.m2/C=-6.64×10-9C

Therefore, the charge on the particle is -6.64×10-9C.

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Most popular questions from this chapter

A small charged ball lies within the hollow of a metallic spherical shell of radius R . For three situations, the net charges on the ball and shell, respectively, are

(1)+4q,0;

(2)−6q,+10q;

(3)+16q,−12q. Rank the situations according to the charge on

(a) the inner surface of the shell and

(b) the outer surface, most positive first.

A spherical ball of charged particles has a uniform charge density. In terms of the ball’s radius R, at what radial distances

(a) inside and

(b) outside the ball is the magnitude of the ball’s electric field equal to14of the maximum magnitude of that field?

Figure 23-36 shows two non-conducting spherical shells fixed in place. Shell 1 has uniform surface charge density+6.0μC/m2on its outer surface and radius 3.0cm; shell 2 has uniform surface charge density +4.0μC/m2on its outer surface and radius 2.0 cm ; the shell centers are separated by L = 10cm. In unit-vector notation, what is the net electric field at x= 2.0 cm ?

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?

Figure 23-46a shows three plastic sheets that are large, parallel, and uniformly charged. Figure 23-46b gives the component of the net electric field along an x-axis through the sheets. The scale of the vertical axis is set byEs=6.0×105N/C. What is the ratio of the charge density on sheet 3 to that on sheet 2?
See all solutions

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