Recent content by oddiseas

Homework Statement I have seen 4 different solutions to this question so I am starting to get confused. A steady current I flows down a long cylindrical wire of radius R. Find the magnetic field, both inside and outside the wire, if (a) the current is uniformly distributed over an...

Homework Statement What current density would produce the vector potential A(r)=(-kmu/2pi)In(r/a) (in the z direction) where k is a constant, in cylindrical coordinates? Homework Equations The Attempt at a Solution i have done this three times and i get zero current...

Homework Statement A square well of length L= 0.6 mm is to be used as a trap for He atoms at 20 K. Consider the values of some of the lowest energy levels of He atoms in a 1-D square well. Explain if it is valid to use the Boltzmann distribution in this situation Homework Equations...

we have been learning ststisticsl physics for the last month and the lecturer has still not explained what entropy is.Other than say "this is the boltman interpretation of entropy" all the info i find on the web seems to say different things for different situations so i was hoping someone...

ok thanks

Homework Statement Show that the curve γ(t)=(t²-t+1,t³-t) has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point. I have found the self intersection. I know that a unit tangent vector is the derivative of each...

Homework Statement say i have fifty keys and 1 is the correct key.With replacement i can modell this as a geometric distribution to find the expectation of the number of bernouli trials required until i pick the correct key.But if there is no replacemnt then the probabilities change so how...

ok thanks

ok thanks, using the additive property i see now that we get f(n)=nf(1) and it is determuned by this value. Is it sufficient for part b to use the multiplicative property, and the fact that the identity in z is 1 and thus f(1) maps to 1 to show that the only homomorphism is the identity map.Or...

i am thinking that we do not have multiplicative inverses because there is no polynomial that would give one, we would need to use a rational function, is this a correct assesmnent?

Homework Statement is the set of all polynomials a ring,and a fieldd.Is is commutative and does it have unity Homework Equations The Attempt at a Solution now if we add or multiply any polynomials we get a polynomial. So it is a ring, but i am not sure what the multiplicative...

but for a homomorphism we have: f(n)=f(1*n)=f(1)*f(n) thus f(1) =1 so how is it completeley determined by f(1), which is always one anyway, i thought it would therefore be totally determined by the domain, depending on whether in is integers or rational numbers etc

i can't find this property anywhere in my notes. Is this a property of homomorphismsm in general or only in the cas on the integers?

Homework Statement Let R be any ring and f:Z→R a homomorphism. a)Show that f is completely determined by the single value f(1) b)Determine all possible homomorphisms f in the case when R = Z. Homework Equations The Attempt at a Solution This question has me totally confused...

I must say that after reading about this concept over the last few days it is one of the most fascinating things. Specificaly the concept of self amplification of spontaneous emission.(SASE) I am wondering is it possible to use a coventional synchronotron as an EFL? Apart from the undulator...