Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Rank the situations of Question 9 according to the magnitude of the electric field
(a) halfway through the shell and
(b) at a point $2 R$ from the center of the shell, greatest first.

The rank of the situations according to magnitude of the electric field halfway through the shell is $1 = 2 = 3$ .
The rank of the situations according to magnitude of the electric field at a point $2 R$ from the center of the shell is $1 = 2 = 3$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data:

A charge ball lies within a hollow metallic sphere of radius R .

The net charges of the ball and the shell for three situations are given.

Step 2: Understanding the concept of electric field of hollow metallic sphere:

Using the electric field concept for a hollow metallic sphere, you can get the required rank of the situations. Due to its properties, the charges of a hollow sphere remain at the surface of the sphere. Thus, the charge inside the shell is zero and so its electric field is also zero. Similarly, the electric field at any point at the surface or above surface is given by the surface charges and the distance of the point from the center of the shell.

Formula:

The electric field at any point outside the hollow metallic sphere,

$E = \frac{k Q}{r^{2}}, r \geq R$ ….. (i)

Where, Q is the outer charge of the shell, K is the Coulomb’s constant, and r is the distance.

Step 3: (a) Calculation of the rank according to magnitude of field halfway through the shell:

The electric field at any point inside a hollow metallic sphere is

$E_{r < R} = 0$

Hence, the rank of the situations according to the electric field at halfway is $1 = 2 = 3$ .

Step 4: (b) Calculation of the rank according to magnitude of field at a point 2r from the center:

Consider a Gaussian surface at a distance $2 R$ from the center. Here, the distance of the point is given by

$r = 2 R$

Thus, the point is outside the shell. So, the magnitude of electric fields for the three situations including its outer charge value is given by,

$E = \frac{k (q_{b a l l} + q_{s h e l l})}{{(2 R)}^{2}}$

Here, R is the radius of the spherical shell, $q_{b a l l}$ is the charge on the ball, and $q_{b a l l}$ is the charge on the shell.

The magnitude of the electric field for situation 1 when the charge on the ball is $+ 4 q$ and on the shell is zero.

$\begin{matrix} E_{1} = \frac{k (q_{b a l l} + q_{s h e l l})}{{(2 R)}^{2}} \\ = \frac{k (+ 4 q + 0)}{{(2 R)}^{2}} \\ = \frac{4 q k}{4 {(R)}^{2}} \\ = \frac{q k}{R^{2}} \end{matrix}$

The magnitude of the electric field for situation 2 when the charge on the ball is $- 6 q$ and on the shell is $+ 10 q$ .

$\begin{matrix} E_{2} = \frac{k (- 6 q + 10 q)}{{(2 R)}^{2}} \\ = \frac{4 q k}{4 {(R)}^{2}} \\ = \frac{q k}{R^{2}} \end{matrix}$

The magnitude of the electric field for situation 3 when the charge on the ball is $+ 16 q$ and on the shell is $- 12 q$ .

$\begin{matrix} E_{3} = \frac{k (+ 16 q - 12 q)}{{(2 R)}^{2}} \\ = \frac{4 q k}{4 {(R)}^{2}} \\ = \frac{q k}{R^{2}} \end{matrix}$

Hence, the rank of the situations according to field value is $1 = 2 = 3$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Rank the situations of Question 9 according to the magnitude of the electric field
(a) halfway through the shell and
(b) at a point $2 R$ from the center of the shell, greatest first.

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of electric field of hollow metallic sphere:

Step 3: (a) Calculation of the rank according to magnitude of field halfway through the shell:

Step 4: (b) Calculation of the rank according to magnitude of field at a point 2r from the center:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Rank the situations of Question 9 according to the magnitude of the electric field (a) halfway through the shell and (b) at a point 2R from the center of the shell, greatest first.

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of electric field of hollow metallic sphere:

Step 3: (a) Calculation of the rank according to magnitude of field halfway through the shell:

Step 4: (b) Calculation of the rank according to magnitude of field at a point 2r from the center:

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics

Rank the situations of Question 9 according to the magnitude of the electric field
(a) halfway through the shell and
(b) at a point $2 R$ from the center of the shell, greatest first.