Chapter 23: Q. 65 (page 657)

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
$\frac{η}{2 ε_{0}} [1 - \frac{z}{\sqrt{z^{2} + R^{2}}}] = \frac{1}{2} \frac{η}{2 ε_{0}}$

Short Answer

Expert verified

(a) A disc with a radius of $R$ and a charge of $Q$ that is uniformly distributed. Discover an equation for the strength of the electric field at a point $P$ on the axis at a distance $z$ from the center.

(b) The solution is $z = \frac{R}{\sqrt{3}}$

Step by step solution

Given information and formula used

Given :

$\frac{η}{2 ε_{0}} [1 - \frac{z}{\sqrt{z^{2} + R^{2}}}] = \frac{1}{2} \frac{η}{2 ε_{0}}$

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:

$E = \frac{σ}{2 ε_{0}}$

( $σ$ is the surface charge density on the disc)

Writing a realistic problem and finding the solution of the problem

(a) Realistic problem :

Given a disc with a radius of $R$ and a charge of $Q$ that is uniformly distributed. Discover an equation for the strength of the electric field at a point $P$ on the axis at a distance $z$ from the center. If

$\frac{η}{2 ε_{0}} [1 - \frac{z}{\sqrt{z^{2} + R^{2}}}] = \frac{1}{2} \frac{η}{2 ε_{0}}$

(b) Solution :

From the previous expression, finding the value of z :

$\frac{η}{2 ε_{0}} [1 - \frac{z}{\sqrt{z^{2} + R^{2}}}] = \frac{1}{2} \frac{η}{2 ε_{0}} \Rightarrow 1 - \frac{z}{\sqrt{z^{2} + R^{2}}} = \frac{1}{2} \Rightarrow \frac{z^{2}}{z^{2} + R^{2}} = \frac{1}{4} \Rightarrow z^{2} + R^{2} = 4 z^{2} \Rightarrow z = \frac{R}{\sqrt{3}}$

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.

Start your free trial

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

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Short Answer

Step by step solution

Given information and formula used

Writing a realistic problem and finding the solution of the problem

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Waves Physics

Modern Physics

Oscillations

Scientific Method Physics

Dynamics

Study anywhere. Anytime. Across all devices.

In Problems 63 through 66 you are given the equation(s) used to solve a problem. For each of thesea. Write a realistic problem for which this is the correct equation(s).b. Finish the solution of the problemη2ε0[1-zz2+R2]=12η2ε0

Short Answer

Step by step solution

Given information and formula used

Writing a realistic problem and finding the solution of the problem

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Waves Physics

Modern Physics

Oscillations

Scientific Method Physics

Dynamics

Study anywhere. Anytime. Across all devices.