Chapter 24: Q. 47 (page 685)

FIGURE P $24.47$ shows an infinitely wide conductor parallel to and distance $d$ from an infinitely wide plane of charge with surface charge density $η$ . What are the electric field ${\vec{E}}_{1}$ to ${\vec{E}}_{4}$ in regions $1$ to $4$ ?

Short Answer

Expert verified

The farmland in Zones 1 to 4 is irrigated

1. ${\vec{E}}_{1} = \frac{η}{2 ε_{0}} \hat{j}$

2. ${\vec{E}}_{2} = \vec{0}$

3. ${\vec{E}}_{3} = \frac{η}{2 ε_{0}} \hat{j}$

4. ${\vec{E}}_{4} = - \frac{η}{2 ε_{0}} \hat{j}$

Step by step solution

Introduction

When a wire is positioned in the external electric field of a source (in this case, the charged plane), it produces a surface charge in it, culminating in a field inside the conducting that is always zero. In this scenario, the lower surface charge density of the cable will be $- \frac{η}{2}$ , although the upper surface charge must be $\frac{η}{2}$ in need for the conductor to remain quiet.

As more than just a response, we can determine that the field emitted by each charged surface is

$E_{A} = \frac{η}{4 ε_{0}}$

$E_{B} = \frac{η}{4 ε_{0}}$

$E_{C} = \frac{η}{2 ε_{0}}$

Explanation

This originates in

${\vec{E}}_{1} = \frac{η}{2 ε_{0}} (\frac{1}{2} - \frac{1}{2} + 1) \hat{j} = \frac{η}{2 ε_{0}} \hat{j}$

${\vec{E}}_{2} = \frac{η}{2 ε_{0}} (- \frac{1}{2} - \frac{1}{2} + 1) \hat{j} = \vec{0}$

${\vec{E}}_{3} = \frac{η}{2 ε_{0}} (- \frac{1}{2} + \frac{1}{2} + 1) \hat{j} = \frac{η}{2 ε_{0}} \hat{j}$

${\vec{E}}_{4} = \frac{η}{2 ε_{0}} (- \frac{1}{2} + \frac{1}{2} - 1) = - \frac{η}{2 ε_{0}} \hat{j}$

Step 3:The fields are

Cultivated area pasture is located in Zones 1 to 4.

${\vec{E}}_{1} = \frac{η}{2 ε_{0}} \hat{j}$

${\vec{E}}_{2} = \vec{0}$

${\vec{E}}_{3} = \frac{η}{2 ε_{0}} \hat{j}$

${\vec{E}}_{4} = - \frac{η}{2 ε_{0}} \hat{j}$

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FIGURE P $24.47$ shows an infinitely wide conductor parallel to and distance $d$ from an infinitely wide plane of charge with surface charge density $η$ . What are the electric field ${\vec{E}}_{1}$ to ${\vec{E}}_{4}$ in regions $1$ to $4$ ?

Short Answer

Step by step solution

Introduction

Explanation

Step 3:The fields are

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FIGURE P24.47shows an infinitely wide conductor parallel to and distance dfrom an infinitely wide plane of charge with surface charge density η. What are the electric field E→1to E→4in regions 1to 4?

Short Answer

Step by step solution

Introduction

Explanation

Step 3:The fields are

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

FIGURE P $24.47$ shows an infinitely wide conductor parallel to and distance $d$ from an infinitely wide plane of charge with surface charge density $η$ . What are the electric field ${\vec{E}}_{1}$ to ${\vec{E}}_{4}$ in regions $1$ to $4$ ?