Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

An electron in a vacuum chamber is fired with a speed of 8300km/stoward a large, uniformly charged plate 75cm away. The electron reaches a closest distance of 15cm before being repelled. What is the plate’s surface charge density?

Short Answer

Expert verified

The plate’s surface charge density is2.8x10-9C/m²

Step by step solution

01

Given information and formula used

Given :

The electron is fired with a speed of : 8300km/s

Distance from the uniformly charged plate : 75cm

The electron reaches a closest distance of : 15cm

Theory used :

The electric field owing to an infinite plane is calculated as follows:

E=σ2ε0

The electron's force

F=eE=eσε0

The electron's work consists of the following:

W=Fd=deσε0d=12mv2deσε0=12mv2

02

Calculating the plate’s surface charge density 

Finding d:

d=d-d=75cm-15cm=60cm=0.6m

Finally, we locate a:

deσε0=12mv2σ=mv2ε02de=(9.11×10-31)×(8.3×106)²×(8.85×10-12)2x0.6x(1.6x10-19)=2.8x10-9C/m²

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A problem of practical interest is to make a beam of electrons turn a 90°corner. This can be done with the parallel-plate capacitor shown in FIGURE. An electron with kinetic energy 3.0×10-17Jenters through a small hole in the bottom plate of the capacitor.

a. Should the bottom plate be charged positive or negative relative to the top plate if you want the electron to turn to the right? Explain.

b. What strength electric field is needed if the electron is to emerge from an exit hole 1.0cmaway from the entrance hole, traveling at right angles to its original direction?

Hint: The difficulty of this problem depends on how you choose your coordinate system.

c. What minimum separation dminmust the capacitor plates have?

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of these

a. Write a realistic problem for which this is the correct equation(s).

b. Finish the solution of the problem

(9.0×109Nm2/C2)2(2.0×10-7C/m)r=25000N/C

The electric field 5.0cmfrom a very long charged wire is ( 2000N/C, toward the wire). What is the charge (in nC) on a 1.0-cm-long segment of the wire?

A sphere of radius R has charge Q. The electric field strength at distancer>RisEi. What is the ratio Ef/Eiof the final to initial electric field strengths if

(a) Q is halved,

(b) R is halved, and

(c) r is halved (but is still>R)? Each part changes only one quantity; the other quantities have their initial values

FIGURE Q23.6shows a hollow soda straw that has been uniformly charged with a positive charge. What is the electric field at the center (inside) of the straw? Explain.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free