Jackson Definition and 103 Threads

Homework Statement I am having some difficulty with Jackson's notation. I am coming from an engineering (not physics) background. First of all, on Page 36 at the bottom of the page, Jackson uses the Dirac delta function d(x-x'). When he integrates his answer is the function at x...

Homework Statement Every time I pick up Jackson I feel dumb :( So in 5.5 chapter about Circular Current Loop, he says: |\vec{r}-\vec{r}'|=[r^2+r'^2-2rr'(\cos\theta\cos\theta'+\sin\theta\sin\theta'\cos\phi')]^{1/2} So it's cosine rule, but how did he got to that sine/cosine thing? It...

Homework Statement There is one thing I'm not getting in this problem. It's about uniformly magnetized sphere. In solving the problem with formula for magnetic potential: \phi_M=-\nabla\cdot\int\frac{\vec{M}}{|\vec{r}-\vec{r}'|}d^3r' At one point a change of variable for...

Homework Statement The expression {\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}} has a volume integral equal to 4\pi for arbitrary "a". Homework Equations The Attempt at a Solution \int_0^R {\int_0^{\pi /2} {\int_0^\pi {{\textstyle{{3{a^2}} \over {{{({a^2} + {r^2})}^{5/2}}}}}...

Homework Statement With a Taylor series expansion of the well-behaved \rho ({\bf{x'}}) around {\bf{x'}} = {\bf{x}}, one finds the Taylor expansion of the charge density to be, \rho ({\bf{x'}}) = \rho ({\bf{x}}) + {\textstyle{1 \over 6}}{r^2}{\nabla ^2}\rho + ... Homework Equations...

Jackson electrodynamics 3rd. p244 I understood that G=\frac{e^{ikR}}{R} is a spetial solution for ( \nabla ^2 + k^2 )G =0 (R>0) . but,why G=\frac{e^{ikR}}/{R} satisfy ( \nabla ^2 + k^2 )G =-4\pi \delta (\mathbf{R}) ? How to normalize the Green function? ( \nabla ^2 + k^2...

Hi, I would like to know if anyone can help me for solving the problem no.26 chapter 2 of Jackson for e&m Thank you

Homework Statement Determine how many quanta with wavelengths between 4000 and 6000 angstroms are emitted per centimeter of path in Lucite by a 1-Mev electron, where the index of refraction for Lucite is 1.50 in this range. This is question 14.16 in Jackson's Classical Electrodynamics...

Homework Statement Jackson Section 5.10, the uniformly magnetized sphere, I'm trying to fill in the steps from his first equation to Equation 5.104. I get the same potential except I am lacking the cos\theta term. My work shown below. Homework Equations The Attempt at a Solution...

Homework Statement I have problems solving the related Laplace equations in the problem Homework Equations \frac{1}{\rho}\frac{\partial}{\partial\rho}\rho\frac{\partial g_m(\rho,\rho^')}{\partial\rho}-m^2g_m(\rho,\rho^')}=-4\pi\frac{\delta(\rho-\rho^')}{\rho} The Attempt at a...

Homework Statement After demonstrating that a set of functions are orthogonal and complete, Jackson presents equations like the ones shown below. I've used the equations for the Legendre series representation as an example, but he does almost the exact same thing with the Bessel functions...

Homework Statement How do you get from (3.25) to (3.26) in Jackson? Homework Equations Equation 3.25: A_l=\left(2l+1\right)\int_0^1P_l\left(x\right)dx Equation 3.26: A_l=\left(-\frac{1}{2}\right)^{\frac{l-1}{2}}\frac{\left(2l+1\right)\left(l-2\right)!}{2\left(\frac{l+1}{2}\right)!}...

Homework Statement A hollow right circular cylinder of radius b has its axis coincident with the z axis and its ends at z=0 and z=L. the potential on the end faces is zero, while the potential on the cylindrical surface is given as V(\varphi,z ). Using the appropriate separation of variables...

Jackson: t-minus three semesters and counting! Okay, help me with this thought-experiment: I was wondering how well-prepared for graduate (Jackson) electromagnetism I would be if I had studied the entirety of Griffith's "Intro...Electrodynamics" one year beforehand. What subject-matter would I...

Homework Statement An electron moves in a helix : \vec{r}(t)=v_{z}t \hat{z}+a e^{i\omega_{0}t}(\hat{x}-i\hat{y}), where a is the radius of the helix and v_{z} the relativistic z-component of the velocity. 1) Find the position vector of the electron in a system of reference that is moving...

Reading Jackson this morning, where it was stated that the Lorentz force equations: \frac{dU^\alpha}{d\tau} = \frac{e}{mc} F^{\alpha\beta} U_\beta are sufficient to describe the motion of a charged particle in an external field, neglecting the effects of radiation. That radiation...

Homework Statement If you have a copy of Jackson handy, this is in the middle of Section 1.7 (p.35 in my book). I'm trying to understand how he gets from Equation 1.30 to the next step (which is an unnumbered equation). Specifically, how is the term in square brackets a Taylor expansion of...

It seems like people are going crazy now that he died. Most of the people that are going insane over it didn't care about him until he died.

I'm starting grad school this fall - direct entry PhD in astronomy & astrophysics. I eventually want to do theoretical cosmology, although I am not sure in what capacity yet. In the 5 years of the program, we're only required to take 4 classes, and they can be pretty much whatever, as long as...

Can someone explain to me how Jackson, on page 42 of the 3rd ed. of Classical Electrodynamics, when he is deriving the interaction energy W_{int} in his example involving two point charges, gets from equation (1.57) to (1.58). I thought about typing up the TeX but I'm sure most of you have this...

http://ca.reuters.com/article/entertainmentNews/idCATRE55O6AK20090625

I would like to know recommendations for the best way to prepare for Jackson's electrodynamics next Fall. I have taken Griffith's E&M as well as the usual undergraduate math (linear algebra, advanced calculus, complex variables, probability). I realize there have been some similar posts to this...

I have a question from jackson 5.26. Details are in my weblog: http://buyanik.wordpress.com/2009/04/19/about-jackson-problem-526/ After anyone have read my weblog post, the question is which problem is true and why? Thanks.

Jackson 2nd editon 6.2 and 3rd edition 5.26 are same questions but given solutions in problems are different. 2nd edition includes c2 (c*c), 3rd edition includes nü/4pi(=c). Which is true and why?

Homework Statement I need some guidance concerning Jackson 6.5c. Specifically I cannot get the -1/3 factor that the statement says I should. Homework Equations Solutions to part a and b which are given in the problem statement. The Attempt at a Solution -I started from the volume...

Homework Statement Jackson 6.4b Homework Equations Multipole expansion especially Eq 4.9 in Jackson which is for a Quadrupole The Attempt at a Solution I found the result in 6.4a. The rho over there tells us that there is a charge density inside the sphere. Since the charge density...

The first time I took Electromagnetics via Jackson I did terribly on account of not knowing the math needed to read the book (I despise the fact that many graduate programs do not specify what math is genuinely needed to read the textbooks they assign). At the time, I had taken 1 course each in...

Homework Statement I can't seem to figure out how he writes down this equation. Specifically: a. Isn't Theta' = 90 degrees. Then why doesn't he write it out explicitly. b. Whats the use of adding the Sin(Theta') if he is going to use a delta function using the Cos c. What is the radius 'a'...

Homework Statement I'm working at the exercise 6.8 of Jackson's Classical Electrodynamics. Here it is : We consider a dielectric sphere of dielectric constant \epsilon and of radius a located at the origin. There is a uniform applied electric field E_0 in the x direction. The sphere rotates...

Can anyone explain to me how Jackson goes from equation 5.20 to 5.21 (Magnetostatics - Derivation of the curl of B in terms of the current density). He says that he's used integration by parts but I can't see how he got rid of the first term (the one that involves integrals only) when...

Hi. In http://www-personal.umich.edu/~pran/jackson/P505/p1s.pdf" solution(page 2) to Jackson 1.5 it is stated that \nabla^2 \left(\frac{1}{r}\right)=-4\pi\delta^3(\mathbf r). But why is this true? \nabla^2\left(\frac{1}{r}\right)=\frac{1}{r^2}\frac{d}{d...

In short: Is a class based on the Jackson text necessary to truly understand electromagnetism? In length: I have heard many people (some on this forum) state that the Jackson text is more of an exercise in mathematical physics and/or is the “hazing” that one must endure to be a PhD in...

Is jackson ridiculously hard? and if so how do people manage doing the problems in the book?

Please help for jackson (3rd. edition) chapter 11 question 12.

Is Jackson's C. E. sufficient for the study of Q.E.D., or is their another book equal in stature on Q.E.D.?

<<Note from Moonbear: I've separated this from the urinal thread since it seems to have become a discussion all it's own. I couldn't resist the title. :redface:>> Jackson Pollock's work was brilliant. Art from that era looks inexplicable to people like Evo, but there is method in the...

Homework Statement There is a realistic circular solenoid of infinite length. Current I flows in it, and there are N turns per unit length. The problem asks to show that just outside the solenoid there exists a magnetic field identical in magnitude and direction as that of a single wire on the...

Homework Statement 9.8a) Show that a classical oscillating eletric dipole p with fields given by (9.18) radiates electromagnetic angular momentum to infinity at the rate \frac{d\mathbf{L}}{dt}=\frac{k^3}{12\pi\epsilon_0}\textrm{Im}[\mathbf{p^*\times p}] Hint: The electromagnetic angular...

Homework Statement A localized electric charge distribution produces an electrostatic field, {\bf E}=-\nabla \phi Into this field is placed a small localized time-independent current density J(x) which generates a magnetic field H. a) show that the momentum of these electromagnetic...

Like Jackson Pollock (!?) "He hit the campus like Jackson Pollock". Said the TV commentator when one boxer was KO-ed last night. Anybody heard that before,what kind of saying is that,what's the logic behind it? If I don't mistake J.Pollock was a well known abstract expressionist painter,but...

The problem and a solution can both be found here. In this problem there is a line charge and two conducting planes at the axis. You use the method of images to solve it. The first three parts are easy enough. The fourth asks what the electric field is far from the origin. I do not know...

I am interested in attempting to work through Jackson over the summer and I am wondering what mathematics backround is necessary before doing this. I have ken calc 1-3, DE, complex analysis (for engineers), and a probability and statistics course. Surprisingly, I have never taken a linear...

I'm a student in a master's program, and of course I am working through the obligatory Jackson textbook. I can't help but wonder how useful this is going to be, how applicable. Let's face it, the book does little to further my insight into the actual physics. It's more of a treatise on...

in the introduction to jackson's classical electrodynamics, he states that the number of photons incident to a 1 square centimeter area in 1 s for a 100W bulb (1 m away) is on the order of 10^15. also he gives a similar quantity for an FM antenna operating at 100W at a frequency of 10^8 Hz...

I'm getting ready to take my graduate class in electrodynamics, and I'm wondering what I can do in the next couple weeks to prepare myself for the torture that is certain to ensue.

How did Michael Jackson change the color of his skin? Someone told me it was through skin pigmentation surgery thanks

I did a search for "Michael" and "Jackson" and "Michael Jackson" but I didn't see a thread but if this is redundant please give me a link because I suck at finding things. It was a tossup between social sciences and politics and world affairs so I put it here. But I need to vent. I haven't...

I've been planning to get myself a minilibrary consisting of the classic books in various subjects. So far I've decided to get Goldstein for classical mechanics and Jackson for electrodynamics. On the top of those I think I should have books of "similiar status" for QM, statistical physics...

My art teacher gave an assignment to us to find 2 examples of some of Jackson Pollock's Figure Drawing, ie art with reconizable human forms in it be it painting, drawing, what have you. Most Jackson Pollock is Know for his abstract stuff, making it very hard for me to find anything that even...

Frank Jackson on "qualia" In "Epiphenomenal Qualia", when Frank Jackson describes qualia he says he thinks there are “certain features of the bodily sensations especially, but also of certain perceptual experiences, which no amount of purely physical information includes.” My question is...