Explanation 1) Concept: For this problem, we can use Ampere’s law by considering a suitable Ampere loop to find the magnetic field at a given point over the specified region. After that, we can find out the current enclosed in the ampere loop. Finally, we get expression for B field for a particular point. 2) Formula: ∮ B → · d s → = μ 0 I e n c l o s e d 3) Given: i) Fig 29.88 shows a cross section of a long conducting coaxial cable, with its radii a, b and c. ii) Equal but opposite currents are uniformly distributed in the two conductors. iii) Radius of central solid cylindrical part of cable c = 0.40 c m = 0.40 × 10 - 2 m iv) Inner radius of outer hollow cylindrical part of cable b = 1.8 c m = 1.8 × 10 - 2 m v) Outer radius of outer hollow cylindrical part of cable a = 2 c m = 2.0 × 10 - 2 m vi) Current through inner and outer cylindrical part i = 120 A flowing in opposite directions 4) Calculations: a) For r < c ∮ B → · d s → = μ 0 I e n c l o s e d B ∮ d s = μ 0 I e n c l o s e d B · 2 π r = μ 0 I e n c l o s e d B = μ 0 I e n c l o s e d 2 π r Now let’s find the current enclosed in the ampere loop of radius r : I e n c l o s e d = π r 2 π C 2 i = r 2 C 2 i So we get B = μ 0 2 π r r 2 C 2 = μ 0 i r 2 π C 2 b) For c < r < b ∮ B → · d s → = μ 0 I e n c l o s e d B ∮ d s = μ 0 I e n c l o s e d B · 2 π r = μ 0 I e n c l o s e d B = μ 0 I e n c l o s e d 2 π r Now let’s find the current enclosed in the ampere loop of radius r : I e n c l o s e d = i , so we get B = μ 0 i 2 π r c) For b < r < a ∮ B → · d s → = μ 0 I e n c l o s e d B ∮ d s = μ 0 I e n c l o s e d B · 2 π r = μ 0 I e n c l o s e d B = μ 0 I e n c l o s e d 2 π r Let’s find the current enclosed in the ampere loop of radius r : I e n c l o s e d = i - i r 2

11th Edition

ISBN: 9781119813293

Author: Halliday

Publisher: WILEY

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Question

Chapter 29, Problem 87P

To determine

To:

find the expression for B(r) with radial distance r in the ranges

a) r<c

b) c<r<b

c) b<r<a

d) r>a

e) Test the B(r ) for a few special cases that occur to you.

f) Plot the function B(r) over the range 0<r<3 cm under certain conditions.

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Chapter 29, Problem 86P

Chapter 29, Problem 88P

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A collection of electric charges that share a common magnitude q (lower case) has been placed at the corners of a square, and an additional charge with magnitude Q (upper case) is located at the center of that square. The signs of the charges are indicated explicitly such that ∣∣+q∣∣∣∣+Q∣∣=∣∣−q∣∣==∣∣−Q∣∣=qQ Four unique setups of charges are displayed. By moving one of the direction drawings from near the bottom to the bucket beside each of the setups, indicate the direction of the net electric force on the charge with magnitude Q, located near the center, else indicate that the magnitude of the net electric force is zero, if appropriate.

A number of electric charges has been placed at distinct points along a line with separations as indicated. Two charges share a common magnitude, q (lower case), and another charge has magnitude Q(upper case). The signs of the charges are indicated explicitly such that ∣∣+q∣∣∣∣+Q∣∣=∣∣−q∣∣==∣∣−Q∣∣=qQ Four different configurations of charges are shown. For each, express the net electric force on the charge with magnitude Q (upper case) as F⃗E=FE,xî where the positive x direction is towards the right. By repositioning the figures to the area on the right, rank the configurations from the most negative value to the most positive value of FE,x.

Chapter 29 Solutions

FUNDAMENTALS OF PHYSICS EXTEND 11E

Ch. 29 - Prob. 1Q Ch. 29 - Prob. 2Q Ch. 29 - Prob. 3Q Ch. 29 - Prob. 4Q Ch. 29 - Prob. 5Q Ch. 29 - Prob. 6Q Ch. 29 - Prob. 7Q Ch. 29 - Prob. 8Q Ch. 29 - Prob. 9Q Ch. 29 - Prob. 10Q

Ch. 29 - Prob. 11Q Ch. 29 - A surveyor is using a magnetic compass 6.1 m below...Ch. 29 - Figure 29-35a shows an element of length ds = 1.00...Ch. 29 - SSM At a certain location in the Philippines,...Ch. 29 - Prob. 4P Ch. 29 - Prob. 5P Ch. 29 - Prob. 6P Ch. 29 - Prob. 7P Ch. 29 - Prob. 8P Ch. 29 - Prob. 9P Ch. 29 - Prob. 10P Ch. 29 - Prob. 11P Ch. 29 - Prob. 12P Ch. 29 - Prob. 13P Ch. 29 - Equation 29-4 gives the magnitude B of the...Ch. 29 - Prob. 15P Ch. 29 - Prob. 16P Ch. 29 - Prob. 17P Ch. 29 - Prob. 18P Ch. 29 - Prob. 19P Ch. 29 - Prob. 20P Ch. 29 - Prob. 21P Ch. 29 - Prob. 22P Ch. 29 - Prob. 23P Ch. 29 - Prob. 24P Ch. 29 - Prob. 25P Ch. 29 - Prob. 26P Ch. 29 - Prob. 27P Ch. 29 - GO Figure 29.56a shows two wires, each carrying....Ch. 29 - Prob. 29P Ch. 29 - Prob. 30P Ch. 29 - Prob. 31P Ch. 29 - GO The current-carrying wire loop in Fig. 29-6a...Ch. 29 - Prob. 33P Ch. 29 - Prob. 34P Ch. 29 - Prob. 35P Ch. 29 - Prob. 36P Ch. 29 - Prob. 37P Ch. 29 - Prob. 38P Ch. 29 - Prob. 39P Ch. 29 - Prob. 40P Ch. 29 - Prob. 41P Ch. 29 - Prob. 42P Ch. 29 - Prob. 43P Ch. 29 - Prob. 44P Ch. 29 - Prob. 45P Ch. 29 - Prob. 46P Ch. 29 - ILW The current density inside a long, solid,...Ch. 29 - Prob. 48P Ch. 29 - Prob. 49P Ch. 29 - A solenoid that is 95.0 cm long has a radius of...Ch. 29 - A 200-turn solenoid having a length of 25 cm and a...Ch. 29 - A solenoid 1.30 m long and 2.60 cm in diameter...Ch. 29 - A long solenoid has 100 turns/cm and carries...Ch. 29 - An electron is shot into one end of a solenoid. As...Ch. 29 - Prob. 55P Ch. 29 - Prob. 56P Ch. 29 - Prob. 57P Ch. 29 - Prob. 58P Ch. 29 - Prob. 59P Ch. 29 - Prob. 60P Ch. 29 - A circular loop of radius 12 cm carries a current...Ch. 29 - Prob. 62P Ch. 29 - Prob. 63P Ch. 29 - Prob. 64P Ch. 29 - A cylindrical cable of radius 8.00 mm carries a...Ch. 29 - Two long wires lie in an xy plane, and each...Ch. 29 - Two wires, both of length L, are formed into a...Ch. 29 - Prob. 68P Ch. 29 - Prob. 69P Ch. 29 - Prob. 70P Ch. 29 - A 10-gauge bare copper wire 2.6 mm in diameter can...Ch. 29 - A long vertical wire carries an unknown current....Ch. 29 - Prob. 73P Ch. 29 - The magnitude of the magnetic field at a point...Ch. 29 - Prob. 75P Ch. 29 - Prob. 76P Ch. 29 - Prob. 77P Ch. 29 - A long wire carrying 100 A is perpendicular to the...Ch. 29 - A long, hollow, cylindrical conductor with inner...Ch. 29 - A long wire is known to have a radius greater than...Ch. 29 - Prob. 81P Ch. 29 - Prob. 82P Ch. 29 - Prob. 83P Ch. 29 - Three long wires all lie in an xy plane parallel...Ch. 29 - Prob. 85P Ch. 29 - Prob. 86P Ch. 29 - Prob. 87P Ch. 29 - Prob. 88P

Knowledge Booster

To: find the expression for B ( r ) with radial distance r in the ranges a) r < c b) c < r < b c) b < r < a d) r > a e) Test the B ( r ) for a few special cases that occur to you. f) Plot the function B ( r ) over the range 0 < r < 3 c m under certain conditions.

Solution Summary: The author explains how to find the expression for B(r) with radial distance r.

To:

find the expression for B(r) with radial distance r in the ranges

a) r<c

b) c<r<b

c) b<r<a

d) r>a

e) Test the B(r ) for a few special cases that occur to you.

f) Plot the function B(r) over the range 0<r<3 cm under certain conditions.

Want to see the full answer?

Chapter 29 Solutions

To: find the expression for B ( r ) with radial distance r in the ranges a) r &lt; c b) c &lt; r &lt; b c) b &lt; r &lt; a d) r &gt; a e) Test the B ( r ) for a few special cases that occur to you. f) Plot the function B ( r ) over the range 0 &lt; r &lt; 3 c m under certain conditions.

Solution Summary: The author explains how to find the expression for B(r) with radial distance r.

To: find the expression for B(r) with radial distance r in the ranges a) r<c b) c<r<b c) b<r<a d) r>a e) Test the B(r ) for a few special cases that occur to you. f) Plot the function B(r) over the range 0<r<3 cm under certain conditions.

Want to see the full answer?

Chapter 29 Solutions

To: find the expression for B ( r ) with radial distance r in the ranges a) r < c b) c < r < b c) b < r < a d) r > a e) Test the B ( r ) for a few special cases that occur to you. f) Plot the function B ( r ) over the range 0 < r < 3 c m under certain conditions.

To:

find the expression for B(r) with radial distance r in the ranges

a) r<c

b) c<r<b

c) b<r<a

d) r>a

e) Test the B(r ) for a few special cases that occur to you.

f) Plot the function B(r) over the range 0<r<3 cm under certain conditions.