Explanation Given Info: The radius of the cylindrical wire is R . The current through the long cylindrical wire is I 0 . The one side length of the rectangle is W . Formula to calculate the magnetic field by Ampere’s law is, ∮ B → ⋅ d l → = μ 0 I encl (I) μ 0 is the magnetic constant, I encl is the current enclosed in the path, ∮ d l → is the differential length of the cylindrical wire. Formula to calculate the current density in the cylindrical wire is, J = I 0 A I 0 is the current flow in the cylindrical wire, A is the area of the cylindrical wire. Formula to calculate the area of the cylindrical wire is, A = π R 2 R is the radius of the cylindrical wire. Substitute π R 2 for A to find J . J = I 0 π R 2 (II) Refer figure.2. The current I encl enclosed in the cylindrical wire when r < R (inside the conductor) is, I encl = J A (III) Formula to calculate the area of the cylindrical wire when r < R is, A = π r 2 r is the distance from the center of the cylindrical wire. Substitute π r 2 for A in equation (III). I encl = J ( π r 2 ) (IV) Substitute equation (II) in equation (IV). I encl = ( I 0 π R 2 ) ( π r 2 ) = I 0 r 2 R 2 Substitute I 0 r 2 R 2 for I encl in equation (I). ∮ B → ⋅ d l → = μ 0 ( I 0 r 2 R 2 ) Take magnitude for the above equation, | ∮ B → ⋅ d l → | = | μ 0 ( I 0 r 2 R 2 ) | B ∮ d l = μ 0 I 0 r 2 R 2 (V) Substitute 2 π r for ∮ d l in equation (V). B ( 2 π r ) = μ 0 I 0 r 2 R 2 Rearrange the above equation as follows, B = μ 0 I 0 r 2 2 π r R 2 = μ 0 I 0 r 2 π R 2 (VI)

University Physics with Modern Physics (14th Edition)

14th Edition

ISBN: 9780321973610

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

See similar textbooks

Concept explainers

Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

Question

Chapter 29, Problem 29.55P

To determine

The total magnetic flux through a rectangle.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 29, Problem 29.54P

Chapter 29, Problem 29.56P

Students have asked these similar questions

Answer the given question showing step by step by and all necessary working out.

1. The piston in the figure has a mass of 0.5 kg. The infinitely long cylinder is pushed upward at a constant velocity. The diameters of the cylinder and piston are 10 cm and 9 cm, respectively, and there is oil between them with v = 10⁻⁴ m^2/s and γ = 8,000 N/m³. At what speed must the cylinder ascend for the piston to remain at rest?

Hi, 1- Does Quantum physics theory and Newtowin physics right or wrong about Gravity? 2- How can we rewrite Quantum physics and Newtowin physics Equations?

Chapter 29 Solutions

University Physics with Modern Physics (14th Edition)

Ch. 29.2 - The accompanying figure shows a wire coil being...Ch. 29.3 - (a) Suppose the magnet in Fig. 29.14a were...Ch. 29.4 - The earths magnetic field points toward (magnetic)...Ch. 29.5 - If you wiggle a magnet back and forth in your...Ch. 29.6 - Prob. 29.6TYU Ch. 29.7 - Prob. 29.7TYU Ch. 29 - A sheet of copper is placed between the poles of...Ch. 29 - Prob. 29.2DQ Ch. 29 - Prob. 29.3DQ Ch. 29 - Prob. 29.4DQ

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

The total magnetic flux through a rectangle.

Solution Summary: The author explains how the magnetic flux through a rectangle is mu_0IW4pi.

Concept explainers

The total magnetic flux through a rectangle.

Want to see the full answer?

Chapter 29 Solutions