Help with Griffiths Electrodynamics

In summary: GPA from grad school...)In summary, someone has a problem with 5.42 in Griffiths Electrodynamics and is looking for a solution. They found one online, but it's not the same answer as the book.
  • #1
sinyud
23
0
I've been brushing up on electrodynamics before I start grad school when I encountered problem 5.42 in Griffith's Electrodynamics. I can get everything correct except the coefficient to work out. Any one know where I can find a solution to this problem?
----------------------------------------
"Not everyone has the book"

I never thought of that. Thanks for the advice. Well,

The problem. A spinning spherical shell with radius "R" and constant charge density "sigma" is rotating with angular velocity "w" in the z direction. What is the magnetic force between the nothern hemisphere and the southern hemisphere (I'm assuming north is on the positive side of the z axis, and south is the negative side of the z axis)?

Thanx
BTW has anyone been looking at the Google problems advertised in the Physical Review?
 
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  • #2
It might help if you said what the problem is - not everyone would have a copy of that particular text.
 
  • #3
I have a solution manual that I can sell you.

please email me:

spock0149@hotmail.com

thanks.
 
  • #4
Problem:

Calculate the magnetic force of attraction between the northern and southern hemispheres of a spinning charged spherical shell. (ex. 5.11)

My Solution:
Look at example 5.11 a the book. It is calculated that the field in the spherical shell is uniform:
[tex]B=\frac{2}{3}\mu_0\sigma R \omega[/tex]
If you displaced the hemispheres by a tiny bit [tex]\Delta x[/tex]
you create a gap of volume [tex]\pi R^2 \Delta x[/tex]
We can assume the field stay more of less uniform. (This is not an approximation when we take the limit later).
So the energy in the field in the gap is: (took me a while to look up the eqn for T, energy density, in SI unit:)
[tex]\Delta U=T\times \Delta V=\frac{1}{2}\frac{B^2}{\mu_0}\times \pi R^2 \Delta x[/tex]
[tex]\Delta U=\frac{1}{2}\times\frac{4}{9}\mu_0 \sigma^2 R^4 \omega^w \pi \Delta x[/tex]
So the force is:
[tex]F=-\frac{\Delta U}{\Delta x}=-\frac{2}{9}\pi \mu_0 \sigma^2 R^4 \omega^2[/tex]

...Interesting, I didn't get the factor of [tex]\frac{1}{4}[/tex] either...
Is this what you got?
 
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  • #5
Hi, I'm having trouble with part b of problem 5.46 from the same text. Any help would be nice :-D

Problem 5.46: Magnetic field on the axis of a ciruclar current loop is far from uniform (it falls off sharply with increasing z). You can produce a more nearly uniform field by using two such loops a distance d apart.

part b: Find d such that second partial derivative of B with respect to z is zero when z = 0.

I can get it so that the second partial derivative equals zero, but my answer does not match the book's answer.
 
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  • #6
iMook said:
Hi, I'm having trouble with part b of problem 5.46 from the same text. Any help would be nice :-D

Problem 5.46: Magnetic field on the axis of a ciruclar current loop is far from uniform (it falls off sharply with increasing z). You can produce a more nearly uniform field by using two such loops a distance d apart.

part b: Find d such that second partial derivative of B with respect to z is zero when z = 0.

I can get it so that the second partial derivative equals zero, but my answer does not match the book's answer.
Hey!

Here is my solution:


From a)
Let u be the permeability of free space
B=u*I/2*R^2(1/(R^2+(z+d)^2)^3/2+1/(R^2+(z-d)^2)^3/2)
dB/dz=-3u*I/2*R^2((z+d)/(R^2+(z+d)^2)^5/2+(z-d)/(R^2+(z-d)^2)^5/2)
For simplity let H=(z+d)/(R^2+(z+d)^2)^5/2+(z-d)/(R^2+(z-d)^2)^5/2
when dH/dz=0 is d^2B/dB^2=0
dH/dz=[1/(R^2+(z+d)^2)^5/2+(z+d)*d/dz(1/(R^2+(z+d)^2)^5/2)+
1/(R^2+(z-d)^2)^5/2+(z-d)*d/dz(1/(R^2+(z-d)^2)^5/2)]=...=
[1/(R^2+(z+d)^2)^5/2-5(z+d)^2/(R^2+(z+d)^2)^5/2+1/(R^2+(z-d)^2)^5/2-5(z-d)^2/(R^2+(z-d)^2)^5/2]

Gives
dH/dz(0)=2/(R^2+d^2)^5/2-10d^2/(R^2+d^2)^7/2=0

And d=R/2 ->B(0)=u*I/2*R^2(2/(R^2+1/4R^2)^3/2)=8u*I/(5*sqrt(5)*R) And this equals the answer in my book.

I hope this will help you
 
  • #8
Speaking of griffiths - if anyone comes up with a stumper nobody here can solve, he's my current physics prof, and I talk to him on a daily basis. You wouldn't believe how much his writing sounds like his talking :)
 
  • #9
Ehh, another Reedie :). . .

I'm not too sure David'd be happy to hear of these solution manuals floating around in cyberspace
 
  • #10
Duarh said:
Ehh, another Reedie :). . .

I'm not too sure David'd be happy to hear of these solution manuals floating around in cyberspace

Indeed. I hope most of the tough parts are left "as an exercise for the reader" :)
 
  • #11
How is Griffiths as a prof anyway? It's kind of cool having him be your professor... he's pretty much cornered the undergrad physics textbook market on QM ad E&M I think.

I'm glad John David Jackson is retired though. I wouldn't want to take E&M from him! (That is, if I only wanted a high grade)
 
  • #12
His "Introduction to particle physics" is pretty swell as well.
 
  • #13
He's fun as a prof, explains things in detail and so on, and keeps the informal attitude that's prevalent throughout his books. Sometimes he goes just a bit slow, but I guess that's connected with his wish to be as clear as possible about everything - he does make sure you're grasping what's going on. Funny thing is, though, even though I'm a physics major, I've only really taken what is pretty much a mathematical methods class from him, so I don't know that well what he'd be like in a real physics course. Will find out next year.
 

What is Griffiths Electrodynamics?

Griffiths Electrodynamics is a textbook written by David J. Griffiths that covers the fundamental principles and concepts of electromagnetism, including electrostatics, magnetostatics, electromagnetic waves, and special relativity.

Who is the target audience for Griffiths Electrodynamics?

The target audience for Griffiths Electrodynamics is undergraduate and graduate students in physics and engineering who have a strong foundation in calculus and classical mechanics.

What topics are covered in Griffiths Electrodynamics?

Griffiths Electrodynamics covers topics such as vector calculus, electric and magnetic fields, electromagnetic potentials, Maxwell's equations, electromagnetic waves, and special relativity.

Is Griffiths Electrodynamics a good resource for self-study?

Yes, Griffiths Electrodynamics is a highly recommended textbook for self-study as it provides clear explanations, examples, and exercises to help students understand and apply the concepts of electromagnetism.

Are there any recommended prerequisites for studying Griffiths Electrodynamics?

It is recommended to have a strong foundation in calculus, classical mechanics, and basic electricity and magnetism before studying Griffiths Electrodynamics. Some familiarity with differential equations and vector calculus is also helpful.

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