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Using Eqs. 2.27 and 2.30, find the potential at a distance

Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths ISBN: 9780321856562 45

Solution for problem 25P Chapter 2

Introduction to Electrodynamics | 4th Edition

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Introduction to Electrodynamics | 4th Edition | ISBN: 9780321856562 | Authors: David J. Griffiths

Introduction to Electrodynamics | 4th Edition

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Problem 25P

Using Eqs. 2.27 and 2.30, find the potential at a distance z above the center of the charge distributions in Fig. 2.34. In each case, compute E = −∇V, and compare your answers with Ex. 2.1, Ex. 2.2, and Prob. 2.6, respectively. Suppose that we changed the right-hand charge in Fig. 2.34a to −q; what then is the potential at P? What field does that suggest? Compare your answer to Prob. 2.2, and explain carefully any discrepancy.

Eqs. 2.27

Eqs. 2.30

Reference example 2.1

Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a).

Reference example 2.1

Find the electric field a distance z above the midpoint of a straight line segment of length 2L that carries a uniform line charge λ (Fig. 2.6).

Reference prob.2.6

Find the electric field a distance z above the center of a flat circular disk of radius R (Fig. 2.10) that carries a uniform surface charge σ.What does your formula give in the limit R→∞? Also check the case z ≫R.

Reference figure 2.10

Reference prob.2.2

Find the electric field (magnitude and direction) a distance z above the midpoint between equal and opposite charges (±q), a distance d apart (same as Example 2.1, except that the charge at x = +d/2 is −q).

Reference example 2.1

Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a).

Step-by-Step Solution:

Step 1 of 5</p>

Part a

We are required to calculate the potential at the point  as given in figure 2.3 (a).

Let us have a look at the following figure.

Therefore, the potential at the point  at a distance z above is,

Step 2 of 5</p>

Part b

From equation 2.30,

Let us check the following figure.

From the equation,

The potential due to uniform line charge,

This is the expression for potential due to the line charge.

Step 3 of 5</p>

Part c

From equation 2.30,

Here,  is surface charge density.

Therefore, the total charge

From the above equation,

This is the required expression for potential due to uniform surface charge.

Calculations of

Step 4 of 5

Chapter 2, Problem 25P is Solved
Step 5 of 5

Textbook: Introduction to Electrodynamics
Edition: 4
Author: David J. Griffiths
ISBN: 9780321856562

The answer to “Using Eqs. 2.27 and 2.30, find the potential at a distance z above the center of the charge distributions in Fig. 2.34. In each case, compute E = ??V, and compare your answers with Ex. 2.1, Ex. 2.2, and Prob. 2.6, respectively. Suppose that we changed the right-hand charge in Fig. 2.34a to ?q; what then is the potential at P? What field does that suggest? Compare your answer to Prob. 2.2, and explain carefully any discrepancy. Eqs. 2.27 Eqs. 2.30 Reference example 2.1Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a). Reference example 2.1Find the electric field a distance z above the midpoint of a straight line segment of length 2L that carries a uniform line charge ? (Fig. 2.6). Reference prob.2.6Find the electric field a distance z above the center of a flat circular disk of radius R (Fig. 2.10) that carries a uniform surface charge ?.What does your formula give in the limit R??? Also check the case z ?R.Reference figure 2.10 Reference prob.2.2Find the electric field (magnitude and direction) a distance z above the midpoint between equal and opposite charges (±q), a distance d apart (same as Example 2.1, except that the charge at x = +d/2 is ?q).Reference example 2.1Find the electric field a distance z above the midpoint between two equal charges (q), a distance d apart (Fig. 2.4a).” is broken down into a number of easy to follow steps, and 237 words. Introduction to Electrodynamics was written by and is associated to the ISBN: 9780321856562. Since the solution to 25P from 2 chapter was answered, more than 274 students have viewed the full step-by-step answer. This full solution covers the following key subjects: distance, reference, Field, fig, Find. This expansive textbook survival guide covers 12 chapters, and 550 solutions. The full step-by-step solution to problem: 25P from chapter: 2 was answered by , our top Physics solution expert on 07/18/17, 05:41AM. This textbook survival guide was created for the textbook: Introduction to Electrodynamics , edition: 4.

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Using Eqs. 2.27 and 2.30, find the potential at a distance

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