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

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

η2ε0[1-zz2+R2]=12η2ε0

Short Answer

Expert verified

(a) A disc with a radius of Rand a charge of Qthat is uniformly distributed. Discover an equation for the strength of the electric field at a point Pon the axis at a distance zfrom the center.

(b) The solution isz=R3

Step by step solution

01

Given information and formula used

Given :

η2ε0[1-zz2+R2]=12η2ε0

Theory used :

The electric field due to a uniformly charged disc at a point very distant from the surface of the disc is given by:

E=σ2ε0

(σ is the surface charge density on the disc)

02

Writing a realistic problem and finding the solution of the problem 

(a) Realistic problem :

Given a disc with a radius of Rand a charge of Qthat is uniformly distributed. Discover an equation for the strength of the electric field at a point Pon the axis at a distance zfrom the center. If

η2ε0[1-zz2+R2]=12η2ε0

(b) Solution :

From the previous expression, finding the value of z :

η2ε0[1-zz2+R2]=12η2ε01-zz2+R2=12z2z2+R2=14z2+R2=4z2z=R3

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

A20cm×20cmhorizontal metal electrode is uniformly charged to +80nC. What is the electric field strength 2.0mmabove the center of the electrode?

A 1.0-mm-diameter oil droplet (density role="math" localid="1649088632675" 900kg/m3 ) is negatively charged with the addition of 25 extra electrons. It is released from rest 2.0mm from a very wide plane of positive charge, after which it accelerates toward the plane and collides with a speed of 3.5m/s. What is the surface charge density of the plane?

What are the strength and direction of the electric field at the position indicated by the dot in FIGUREP23.36? Give your answer (a)in component form and (b)as a magnitude and angle measured cwor ccw(specify which) from the positive x-axis.

Your physics assignment is to figure out a way to use electricity to launch a small 6.0-cm-long plastic drink stirrer. You decide that you’ll charge the little plastic rod by rubbing it with fur, then hold it near a long, charged wire, as shown in FIGURE P23.56. When you let go, the electric force of the wire on the plastic rod will shoot it away. Suppose you can uniformly charge the plastic stirrer to 10nCand that the linear charge density of the long wire is 1.0×10-7C/m. What is the net electric force on the plastic stirrer if the end closest to the wire is 2.0cmaway?

Hint: The stirrer cannot be modeled as a point charge; an integration is required.

Three charges are placed at the corners of the triangle in FIGURE Q23.15. The ++charge has twice the quantity of charge of the two - charges; the net charge is zero. Is the triangle in equilibrium? If so, explain why. If not, draw the equilibrium orientation.

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