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I=\int J.dS = \int (\nabla \times M).dS = 4\pi R^{2}M Is this correct without B_{applied} ? If so, what happens when B_{applied} is present?

Sorted! Its I=M X n

Homework Statement \psi(x)=\frac{3}{5}\chi_{1}(x)+\frac{4}{5}\chi_{3}(x) Both \chi_{1}(x) \chi_{3}(x) are normalized energy eigenfunctions of the ground and second excited states respectivley. I need to find the 'wavefunction in the energy representation' The Attempt at a Solution...

Homework Statement Consider a sphere of magnetic material with radius R and magnetisation M in an applied field B_{applied}. Find an expression for: a) the total current flowing around the surface of the sphere; b) the net field at the centre of the sphere. Homework Equations...

Homework Statement Write down an expression for the current density per unit length flowing at the surface of a magnetised material. The Attempt at a Solution Any ideas?

That thread has proved helpful - i have cracked the derivatives. Thanks. Another question though, k is the wavenumber right? Is the wavenumber equivalent to the direction of proporgation? I mean, from the solution k, E and B must be orthogonal, but how does this relate to the direction of...

So I am trying to work through the proof why why the direction of proporgation, the E field and B field are all orthogonal to one another. What i have is... E=E_{0}e^{i(k\ \bullet \ r-\omega t)} B=B_{0}e^{i(k\ \bullet \ r-\omega t)} \nabla \times E= -\frac{dB}{dt} \Rightarrow k...

Thanks

Is this true: e^{i(a+bx)}=cos(a+bx)+i sin(a+bx) ?

Homework Statement What is meant by the completeness of eigenfunctions? The Attempt at a Solution I understand the AX(x)=BX(x) where A is the operator, B is the eigenvalue and X(x) the eigenfunction. I cannot find anywhere anything on what is meant by the completeness of...

since no innitial conditions were given i shall take irt that c cannot be found.

so...er...c?

This was merely a typo, the orignal problem still remains...

*Correction made* :)

Latex isn't working on this post so here it is without Latex: Homework Statement Solve the euler differential equation x^{2}y''+3xy'-3y=0 by making the ansatz y(x)=cx^{m}, where c and m are constants. The Attempt at a Solution y(x)=cx^{m} y'(x)=cmx^{m-1} y''(x)=cm(m-1)x^{m-2}...

Homework Statement Solve the euler differential equation \x^{2}y^{''}+3xy'-3y=0 \int_X f = \lim\int_X f_n < \infty by making the ansatz [tex]y(x)=cx^{m}[tex], where c and m are constants. The Attempt at a Solution [tex]y(x)0=c^{m}[tex] [tex]y^{'}(x)=cm^{m-1}[tex]...