Recent content by plmokn2

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Homework Statement if w is the nth root of unity, i.e. w= exp(2pi/n i) show: (1-w)(1-w^2)...(1-w^{n-1})=n Homework Equations The Attempt at a Solution since w^(n-a)= complex congugate of w^a terms on the left hand side are going to pair up to give |1-w|^2 |1-w^2|^2... but I'm...

Thanks.

That's it. Its probably really obvious but how do you know that D has to be the same on both sides of the boundary? Thanks

I think my question was badly worded/ I've probably misused some terminology. I suppose my actual qustion is: Its obvious from the symmetry that for an uncharged nonconducting non-dielectric that if you put a surface charge density s on it the field above is the same magnitude as the field...

Homework Statement Say I have a boundary between two dielectrics then it's easy to show using a gaussian pillarbox that: D(1)-D(2)=free surface charge density=s where D(1) is the component of the first medium normal to the surface. But suppose that there's nothing else apart from two...

solved Thanks

opps I forgot an m in the answer: sorry. Thanks, I've solved it now.

[SOLVED] derivative of a cross product Homework Statement In some lecture notes I'm reading they jump straight from \frac{d}{d\mathbf{r}}( \frac{m}{2} |\mathbf{\omega}\times\mathbf{r}|^2) to \mathbf{r}\omega^2-\mathbf{\omega}(\mathbf{\omega}.\mathbf{r}) Homework Equations The...

Thanks for your replies, sorry for the slightly ambiguious question.

I know that if a particle is in a spherically symetric potential its angular momentum will be conserved, but what about if somehow we manage to produce say an elliptically symmetric potential? Will the particle then have a momentum along the curve of the ellipse conserved? Thanks

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Homework Statement I came across a slightly unusual question today. It started out fine, just asking me to derive a maxwell relation but then asked under what conditions is this relationship valid. Homework Equations The Attempt at a Solution In deriving the relation I need to assume U...

Homework Statement Why is is the for physical applications of the spherical harmonics |m| must be less than or equal to l, with both being integers? Homework Equations Y(m,l)=exp(im phi)P{m,l}(cos theta) Hopefully my notation is clear, if not please say. The Attempt at a Solution Well...