Chapter 23: Q57P (page 683)

A thin-walled metal spherical shell has radius $0.25 cm$ and charge $2.88 x 10^{4} N / C$ . Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.

Short Answer

Expert verified

a) The magnitude of the electric fieldinside the shell is zero

b) The magnitude of the electric field just outside the shell is $2.88 x 10^{4} N / C$ .

c) The magnitude of the electric field 3.00 m from the center is $200 N / C$

Step by step solution

Listing the given quantities

spherical shell has a radius of 25.0 cm and charge $2.00 x 10^{- 7} C$

Understanding the concept of electric field

Applying the concept of electric field for spherical shells we get the magnitude of the electric field.

Formula:

$E = \frac{|q|}{4 {πε}_{0}} \frac{1}{r^{2}}$

(a) Calculation of the magnitude of the electric field inside the shell

For r < R, E = 0

The magnitude of the electric field inside the shell is zero

(b) Calculation of the magnitude of the electric field just outside the shell

For r slightly greater than R,

$E = \frac{|q|}{4 {πε}_{0}} \frac{1}{r^{2}} = \frac{q}{4 {πε}_{0} R^{2}} = \frac{(9 \times 10^{9} N . m^{2} / C^{2}) (2.00 \times 10^{- 7} C)}{{(0.250 m)}^{2}} = 2.88 \times 10^{4} N / C$

The magnitude of the electric field just outside the shell is $2.88 \times 10^{4} N / C$ .

(c) Calculation of the magnitude of the electric field 3.00 m from the shell

For r > R

$E = \frac{|q|}{4 {πε}_{0}} \frac{1}{r^{2}} = E_{R} {(\frac{R}{r})}^{2} = (2.88 \times 10^{4} N / C) {(\frac{0.250 m}{3.00 m})}^{2} = 200 N / C$

The magnitude of the electric field 3.00 m from the center is $200 N / C$

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.

A thin-walled metal spherical shell has radius $0.25 cm$ and charge $2.88 x 10^{4} N / C$ . Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of electric field

(a) Calculation of the magnitude of the electric field inside the shell

(b) Calculation of the magnitude of the electric field just outside the shell

(c) Calculation of the magnitude of the electric field 3.00 m from the shell

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Oscillations

Magnetism

Geometrical and Physical Optics

Circular Motion and Gravitation

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A thin-walled metal spherical shell has radius0.25cmand charge 2.88x104N/C. Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.

Short Answer

Step by step solution

Listing the given quantities

Understanding the concept of electric field

(a) Calculation of the magnitude of the electric field inside the shell

(b) Calculation of the magnitude of the electric field just outside the shell

(c) Calculation of the magnitude of the electric field 3.00 m from the shell

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Oscillations

Magnetism

Geometrical and Physical Optics

Circular Motion and Gravitation

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

A thin-walled metal spherical shell has radius $0.25 cm$ and charge $2.88 x 10^{4} N / C$ . Find Efor a point (a) inside the shell, (b) just outside it, and (c)from the center.