Engineering Electromagnetics
Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
Question
Book Icon
Chapter 7, Problem 7.31P
To determine

(a)

The total magnetic flux crossing plane ϕ=0,0<z<1.

Expert Solution
Check Mark

Answer to Problem 7.31P

   ϕa=0.392μWb

Explanation of Solution

Given:

Total current carried by cylindrical shell is I=50A

Shell is defined by 1cm<ρ<1.4 cm.

The plane is ϕ=0,0<z<1.

   0<ρ<1.2cm

Calculation:

The current density can be calculated as

   J=Iπr2az

   J=50π[ ( 1.4× 10 2 ) 2 ( 1.0× 10 2 ) 2]azJ=1.66×105azA/m2

The value of current density is 0 when the radii is less than 1 cm.

Applying Ampere's Circuital law, the value of Hϕ at the give radius will be

   2πρHϕ=Iencl=02π 10 2 ρ 1.66× 10 5 ρ d ρ dϕHϕ=8.30×104(ρ2 10 4)ρA/m(102m<ρ<1.4×102m)

As B=μ0H

   B=0.104(ρ2 10 4)ρaϕWb/m2

Now,

   ϕa= B.dS= 0 1 10 2 1.2× 10 2 0.104[ ρ 10 4 ρ ]dρdz ϕa=0.104[( 1.2× 10 2 )21042104ln(1.21.0)]ϕa=3.92×107Wbϕa=0.392μWb

To determine

(b)

The total magnetic flux crossing plane ϕ=0,0<z<1.

Expert Solution
Check Mark

Answer to Problem 7.31P

   ϕb=1.49μWb

Explanation of Solution

Given:

Total current carried by cylindrical shell is I=50A

Shell is defined by 1cm<ρ<1.4 cm.

The plane is ϕ=0,0<z<1.

   1<ρ<1.4cm

Calculation:

The current density can be calculated as

   J=Iπr2az

   J=50π[ ( 1.4× 10 2 ) 2 ( 1.0× 10 2 ) 2]azJ=1.66×105azA/m2

The value of current density is 0 when the radii is less than 1 cm.

Applying Ampere's Circuital law, the value of Hϕ at the give radius will be

   2πρHϕ=Iencl=02π 10 2 ρ 1.66× 10 5 ρ d ρ dϕHϕ=8.30×104(ρ2 10 4)ρA/m(102m<ρ<1.4×102m)

As B=μ0H

   B=0.104(ρ2 10 4)ρaϕWb/m2

Now,

   ϕb= B.dS= 0 1 10 2 1.4× 10 2 0.104[ ρ 10 4 ρ ]dρdz ϕb=0.104[( 1.4× 10 2 )21042104ln(1.41.0)]ϕb=1.49×106Wbϕb=1.49μWb

To determine

(c)

The total magnetic flux crossing plane ϕ=0,0<z<1.

Expert Solution
Check Mark

Answer to Problem 7.31P

   ϕc=27μWb

Explanation of Solution

Given:

Total current carried by cylindrical shell is I=50A

Shell is defined by 1cm<ρ<1.4 cm.

The plane is ϕ=0,0<z<1.

   1.4cm<ρ<20cm

Calculation:

The current density can be calculated as

   J=Iπr2az

   J=50π[ ( 1.4× 10 2 ) 2 ( 1.0× 10 2 ) 2]azJ=1.66×105azA/m2

The value of current density is 0 when the radii is less than 1 cm.

Applying Ampere's Circuital law, the value of Hϕ at the give radius will be

   2πρHϕ=Iencl=02π 10 2 ρ 1.66× 10 5 ρ d ρ dϕHϕ=8.30×104(ρ2 10 4)ρA/m(102m<ρ<1.4×102m)

As B=μ0H

   B=0.104( ( 1.4× 10 2 ) 2 10 4 )ρaϕB= 10 5ρaϕWb/m2

Now,

   ϕc= B.dS= 0 1 1.4× 10 2 20× 10 2 10 5 ρ dρdz ϕc=105ln(201.4)ϕc=2.7×105Wbϕc=27μWb

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Answer all the questions  What is the minimum value of capacitor C1 required such that Vfiltered does not drop below 8 V?  Use the design equation(but make sure you use the right “frequency” and the correct ripple voltage). Show your calculations. Display your circuit in circuit js.   Display Vsecondary (can use the voltage across the added 100 kΩ resistor) and Vfiltered in a “Combined Scope”.  Display VDC in a separate scope:   a) Turn on “Max Scale”, “Show Peak Value” and “Show Negative Peak Value”: b) Run the simulator and adjust the window and simulation speed and time step to be able to see a couple of cycles.  Include a screen capture Document the minimum and maximum values for Vfiltered in your lab report.  Is Vfiltered maintained to be above 8 V?  By how much?  Why?  Explain the waveform shape captured Vfiltered.  It may help your understanding to rerun the simulation with C1 removed and compare that waveform for Vfiltered to that captured
A Three-phase, 3.3 kV, Y connected, 500 kVA, 16 salient pole rotor alternator. The direct and quadrature axis synchronous reactance are 8 and 50/ph respectively. The machine is supplying a load of 350 kVA at 0.8 power factor lagging, Determine: 1. Power angle. 2. Percentage Voltage regulation. 3. Developed power. 4. Reluctance power
A Three-phase, 12 pole, Y-connected alternator has 108 slots and 14 conductors per slot. The windings are (5/6th) pitched. The flux per pole is 57 mWb distributed sinusoidally over the pole. If the machine runs at 500 r.p.m., determine the following: (a) The frequency of the generated e.m.f., (b) The distribution factor, (c) The pitch factor, and (d) The phase and line values of the generated e.m.f.?

Chapter 7 Solutions

Engineering Electromagnetics

Knowledge Booster
Background pattern image
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:PEARSON
Text book image
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:9781337900348
Author:Stephen L. Herman
Publisher:Cengage Learning
Text book image
Programmable Logic Controllers
Electrical Engineering
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education
Text book image
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:9780078028229
Author:Charles K Alexander, Matthew Sadiku
Publisher:McGraw-Hill Education
Text book image
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Text book image
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,