Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B= x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B)=- dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: ds- -=√√2 dr sin(1/4)

A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B= x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B)=- dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: ds- -=√√2 dr sin(1/4)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question
A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B-x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B) dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: dr -=√√2 dr sin(1/4)
Transcribed Image Text:A wire carrying a current /= 27.0 A is bent into the shape of an exponential spiral. Its polar coordinate is described by r = exp(0) from 0-0 to 0-2 as shown in the figure. dr ds B-x/4 To complete the loop, the ends of the spiral are connected by a straight wire along the x axis. Find the magnitude of the magnetic field B at the origin. Suggestions: Although this problem may look daunting at first, remember that the Biot-Savart law is a good starting point to find the magnetic field due to a given current distribution. The simple exponential dependence of the path on the angle should give rise to an integral that is easy to solve. Also, it may help to know that the angle ẞ between a radial line and its tangent line at any point on the curve r = f(0) is related to the function in the following way: tan(B) dr di Thus, in the case of r = exp(0), tan(B)=1 and ẞ=4. Therefore, the angle between the line element vector ds and the radial unit vector r^ is -ẞ=. Additionally, this gives: dr -=√√2 dr sin(1/4)
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Magnetic moment
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS