Holooly Plus Logo
Holooly Plus Logo

Question 23.38: In Fig. 23-48a, an electron is shot directly away from a uni......

In Fig. 23-48a, an electron is shot directly away from a uniformly charged plastic sheet, at speed v_s = 2.0 × 10^5 m/s. The sheet is nonconducting, flat, and very large. Figure 23-48b gives the electron’s vertical velocity component v versus time t until the return to the launch point. What is the sheet’s surface charge density?

1360823-Figure 23.48
Step-by-Step
The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.
Report Answer

The field due to the sheet is E=\frac{\sigma}{2 \varepsilon_0} . The force (in magnitude) on the electron (due to that field) is F = eE, and assuming it’s the only force then the acceleration is

a=\frac{e \sigma}{2 \varepsilon_0 m}=\text { slope of the graph }\left(=2.0 \times 10^5 \,m / s \text { divided by } 7.0 \times 10^{-12}\, s \right) \text {. }

Thus we obtain \sigma=2.9 \times 10^{-6}\, C / m ^2 .

Related Answered Questions

Question: 23.49

In Fig. 23-54, a solid sphere of radius a = 2.00 cm is concentric with a spherical conducting shell of inner radius b = 2.00a and outer radius c = 2.40a. The sphere has a net uniform charge q1=+5.00 fC; the shell has a net charge q2=-q1.What is the magnitude of the electric field at radial distance ...

Verified Answer:

At all points where there is an electric field, it...
Question: 23.81

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 to 1/4 of the maximum magnitude of that field? ...

Verified Answer:

(a) The field maximum occurs at the outer surface:...
Question: 23.80

Charge of uniform surface density 8.00 nC/m² is distributed over an entire xy plane; charge of uniform surface density 3.00 nC/m² is distributed over the parallel plane defined by z = 2.00 m. Determine the magnitude of the electric field at any point having a z coordinate of (a) 1.00 m and ...

Verified Answer:

The field due to a sheet of charge is given by Eq....
Question: 23.79

Water in an irrigation ditch of width w = 3.22 m and depth d = 1.04 m flows with a speed of 0.207 m/s. The mass flux of the flowing water through an imaginary surface is the product of the water’s density (1000 kg/m³) and its volume flux through that surface. Find the mass flux through the ...

Verified Answer:

(a) The mass flux is w d \rho ν=(3.22 \,m ...
Question: 23.12

Figure 23-36 shows two nonconducting spherical shells fixed in place. Shell 1 has uniform surface charge density +6.0 μC/m² on its outer surface and radius 3.0 cm; shell 2 has uniform surface charge density +4.0 μC/m² on its outer surface and radius 2.0 cm; the shell centers are separated by ...

Verified Answer:

We note that only the smaller shell contributes a ...
Question: 23.37

A square metal plate of edge length 8.0 cm and negligible thickness has a total charge of 6.0 × 10^-6 C. (a) Estimate the magnitude E of the electric field just off the center of the plate (at, say, a distance of 0.50 mm from the center) by assuming that the charge is spread uniformly over the two ...

Verified Answer:

THINK To calculate the electric field at a point v...
Question: 23.36

Figure 23-47 shows cross sections through two large, parallel, nonconducting sheets with identical distributions of positive charge with surface charge density σ = 1.77 × 10^-22 C/m². In unit-vector notation, what is E at points (a) above the sheets, (b) between them, and (c) below them? ...

Verified Answer:

According to Eq. 23-13 the electric field due to e...
Question: 23.35

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 by Es=6.0 × 10^5 N/C. What is the ratio of the charge density on sheet 3 ...

Verified Answer:

In the region between sheets 1 and 2, the net fiel...
Question: 23.34

In Fig. 23-45, a small circular hole of radius R = 1.80 cm has been cut in the middle of an infinite, flat, nonconducting surface that has uniform charge density σ = 4.50 pC/m². A z axis, with its origin at the hole’s center, is perpendicular to the surface. In unit-vector notation, what is the ...

Verified Answer:

The charge distribution in this problem is equival...
Question: 23.20

Flux and conducting shells. A charged particle is held at the center of two concentric conducting spherical shells. Figure 23-39a shows a cross section. Figure 23-39b 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 ...

Verified Answer:

Equation 23-6 (Gauss’ law) gives \varepsil...