{"id":71,"date":"2021-02-25T08:22:43","date_gmt":"2021-02-25T08:22:43","guid":{"rendered":"https:\/\/tutorsnest.com\/blog\/?p=71"},"modified":"2021-02-25T08:22:46","modified_gmt":"2021-02-25T08:22:46","slug":"advanced-physics-homework-help-free","status":"publish","type":"post","link":"https:\/\/tutorsnest.com\/blog\/advanced-physics-homework-help-free\/","title":{"rendered":"Advanced Physics Homework Questions and Answers \u2013 Get Expert Solutions to Physics Questions at tutorsnest.com in 6 hours!"},"content":{"rendered":"\n

Quiz 1.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

Let u:R3\u00d7R\u2192R3 be flow velocity of incompressible fluid. Let fluid be subject to potential force \u2212\u2207\u03c7. To prove
ddt\u222bV12\u03c1\u27e8u,u\u27e9dV+\u222b\u2202VH\u27e8u,n\u27e9dA=0where H:=12\u03c1\u27e8u,u\u27e9+p+\u03c7, and notation \u27e8x,y\u27e9 denote standard inner product on R3.<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

fluid dynamic, euler’s equation of the motion<\/p>\n\n\n\n

DuDt=\u2212\u2207p\u03c1\u2212\u2207\u03c7I re-write the Euler equation for incompressible fluid using suffix notation
\u2202ui\u2202t+uj\u2202ui\u2202xj+\u2202\u2202xi(p\u03c1+\u03c7)=0what theorems applies to the problem?<\/p>\n\n\n\n

Quiz 2.<\/strong><\/p>\n\n\n\n

A rectangular coil with a height a, width b, of copper wire with a diameter of d with a number of N-\u00bd threads (or turns or loops, not sure which is the proper word) (the last thread\/loop is only half) is mounted on the vertical conductive and elastic fiber (Pic. A \u2212 4).

Pic A-4 (I’m attaching the picture)
The coil can deflect\/deviates about a vertical axis given by the fiber. The coil is located in a homogeneous magnetic field with induction B in the horizontal direction. The coil is connected to a power supply with a voltage U. The current I of the coil is given by the resistance of the R resistor.
When switch S is switched off \u2013( at rest), the plane of the coil with the direction of the magnetic field forms a zero angle \u03b10 (\u03b1 = 0). If we move the coil from the equilibrium position by a small angle \u03b1 and release it, it will oscillate around the equilibrium position with the frequency f0.
After switching on the switch, the current I1 starts to go through the electrical circuit.
a) After stabilization of the coil oscillations, the new equilibrium position of the coil is given by the angle \u03b11 of deflection from the initial position. Write the equation for the angle \u03b11
b) After a small deflection from the new equilibrium position and release, the coil starts to oscillate with frequency f1. Determine the frequency f1 as a function of the angle \u03b11.
c) For a given current I1, the angle \u03b11 = fa (B) is a function of the induction B and the frequency f1 = fb (\u03b11) is a function of the angle \u03b11. Plot graphs of both functions for given values.
d) This way can be measured the horizontal component Bh of magnetic field induction. Determine the induction of Bh using the constructed graphs from the measured values I1 = 2.0A, f0 = 10Hz and f1 = 300Hz and the given coil parameters.
Solve the problem in general and then for values: N = 5, a = 10 cm, b = 10 cm, d = 0.20 mm, I1 = 2.0 A<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

Fm=B*I*l*sin\u03b1
f=1\/T
v=s\/T –>T=s\/v
–> f=v\/s<\/p>\n\n\n\n

Quiz 3.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

please see below<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

please see below<\/p>\n\n\n\n

For one-dimensional binding potential, a unique energy corresponds to a unique quantum state of the bound particle. In contrast, a particle of unique energy bound in a three-dimensional potential may be in one of several different quantum states. For example, suppose that the three-dimensional box has edges of equal lengths a=b=c, so that it is a cube. Then the energy states are given by
E=h28ma2(nx2+ny2+nz2),nx,ny,nz=1,2,3,4…

(a) what is the lowest possible value for the energy E in the cubical box? show that there is only one quantum state corresponding to this energy (that is, only one choice of the set nx,ny,nz).

(b) What is the second-lowest energy E? Show that this value of energy is shared by three distinct quantum states. Given the probability function |\u03c8|2 for each of these states, could they be distinguuished from one another?

(c) let n2=nx2+ny2+nz2 be an integer proportional to a given permitted energy. List the degeneracies for energies corresponding to n2=3,6,9,11,12. Can you find a value of n2 for which the energy level is sixfold degenerate?



(a) the lowest possible value for E is
E=h28ma2(12+12+12)=3h28ma2
where the quantum state corresponding to this energy is (nx,ny,nz)=(1,1,1).

(b)the second lowest energy E is
E=h28ma2(22+12+12)=3h24ma2
shared by three distinct quantum states (nx,ny,nz)=(2,1,1) or (1,2,1) or (1,1,2).

They cannot be distinguished from one another because|\u03c8|2=sin2(nx\u03c0xa)sin2(ny\u03c0xb)sin2(nz\u03c0xc)where a=b=c, and the three quantum states have identical probabilities.

(c)
n2=3\u21d2(1,1,1)

n2=6\u21d2(2,1,1),(1,2,1),(1,1,2)

n2=9\u21d2(2,2,1),(2,1,2),(1,2,2)

n2=11\u21d2(3,1,1),(1,3,1),(1,1,3)

n2=12\u21d2(2,2,2)

When nx\u2260ny\u2260nz, the number of degeneracies are given by the number of permutations of nx,ny,nz.

<\/p>\n\n\n\n

Quiz 4.<\/strong><\/p>\n\n\n\n


A proton beam of kinetic energy 20 MeV enters a dipole magnet 2 m in length.

How strong must the field be to deflect the beam by 10 degrees?<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

F = qvB<\/p>\n\n\n\n

I haven’t taken a physics courses in some time and I’m having trouble getting started with this textbook question. I know that there will be relativistic effects present, but I can deal with that. The problem is how I can approach the problem. I initially thought of a geometric way to set up the problem where I simply assume magnetic field will exert a force uniformly:<\/p>\n\n\n\n


But I’m not sure if this will work out since the magnetic field will technically induce a circular motion. Any guidance would be greatly appreciated!<\/p>\n\n\n\n

Quiz 5.<\/strong><\/p>\n\n\n\n

Calculate the Energy Levels of an Electron in a Finite Potential Well<\/h6>\n\n\n\n

Quiz 6.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

psb<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

psb<\/p>\n\n\n\n

The equation\u210f22md2udr2\u2212Ze2ru=Eugives the schrodinger equation for the spherically symmetric functions u=r\u03c8 for a hydrogen-like atom.

In this equation, substitute an assumed solution of the form u(r)=(Ar+Br2)e\u2212br and hence find the values of b and the ratio B\/A for which this form of solution satisfies the equation. Verify that it corresponds to the second energy level, with E=Z2\/4 times the groud-state energy of hydrogen, and with B\/A=\u2212Z\/2a0 where a0 is the Bohr radius for hydrogen. What is the value of the coefficient b in terems of a0?

effort:

given
E1=mZ2e42\u210f2
and
a0=4\u03c0\u210f2Zme2\u21d2B\/A=\u22122Z2\u03c0\u210f2me2
\u210f22m[(A+2Br)e\u2212br\u2212b(Ar+Br2)e\u2212br]\u2212Ze2r(Ar+Br2)e\u2212br=mZ4e48\u210f2(Ar+Br2)e\u2212br
[(\u210f22mr\u2212b\u210f22m\u2212Ze2r)Ar+(\u210f22mr\u2212b\u210f22m\u2212Ze2r)Br2]e\u2212br
(\u210f22mr\u2212b\u210f22m\u2212Ze2r)(Ar+Br2)e\u2212br
b=\u2212m2rZ2e4+h4\u22122mZe2h2rh4
how do you proceed?

The book says the answer isb=Z2a0=2Z2\u03c0\u210f2me2

many thanks \":bow:\" edited with progress<\/p>\n\n\n\n

Quiz 7.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

Illustrate the concept that “the physical state of system A is correlated with the state of system B” by considering the momenta of cars on the M25 at rush-hour and the road over the Nullarbor Plain in the dead of night.<\/p>\n\n\n\n

Quiz 8.<\/strong><\/p>\n\n\n\n

Prove the reflection and transmission coefficients always sum to 1<\/h6>\n\n\n\n

Quiz 9.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

Average Energy density and the Poynting vector of an EM wave<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

energy density of the EM fields, Poynting vector<\/p>\n\n\n\n

Hi,
In Problem 9.12 of Griffiths Introduction to Electrodynamics, 4th edition (Problem 9.11 3rd edition), in the problem, he says that one can calculate the average energy density and Poynting vector as


<\/p>\n\n\n\n


using the formula<\/p>\n\n\n\n



I don’t really understand how to do this. I show my attempt below, but I don’t think it is good. Can someone explain if it is really all there is to it?<\/p>\n\n\n\n

Quiz 10.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

Given the Friedmann\u2013Lemaitre equation for a universe containing only matter and radiation)

(1)aa\u02d92=Cr\u2212ka2


Where a is the dimensionless cosmic scale factor, Cr is simplify a constant and the initial condition (I.C.) is a(0)=0.



a) Solve (1) for a flat universe in terms of the conformal time \u03b7. Then show that the conformal time at matter\u2013radiation equality is given by:


(*)\u03b7eq=2(2\u22121)H0\u22121(\u03a9M)0\u22121\/2aeq1\/2


b) Use this result to show that the horizon at matter\u2013radiation equality corresponds today
to a scale of 16((\u03a9M)0h2)\u22121 Mpc, where h:=H0\/(100km s\u22121Mpc\u22121).<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

N\/A<\/p>\n\n\n\n

a) For a flat universe (k=0), so (1) simplifies to a\u02d92=Cra2. The solution to this first order, separable ODE (given the I.C. a(0)=0) is

(2)a(t)=(4Cr)1\/4t1\/2

We switch to conformal time by means of the change of variables

d\u03b7=dta

So (2) takes the form

(3)a(\u03b7)=(Cr)1\/2\u03b7

But how to go from (3) to (\u2217)?

Before discussing b) I need to understand (\u2217)

Main sources:

– Chapter 38<\/a> in Matthias Blau’s GR notes (attached).
– Chapter 1<\/a> in Daniel Baumann’s notes.<\/p>\n\n\n\n

Quiz 11.<\/strong><\/p>\n\n\n\n

Homework Statement:<\/strong><\/p>\n\n\n\n

Calculate the wavelength for an Ex polarized wave<\/p>\n\n\n\n

Relevant Equations:<\/strong><\/p>\n\n\n\n

Unsure<\/p>\n\n\n\n

Calculate the wavelength for an Ex polarized wave travelling through an anisotropic material with \u03f5\u00af\u00af=\u03f50diag(0.5,2,1) and \u03bc\u00af\u00af=2\u03bc0 in:
a. the y direction
b. the z direction
Leave answers in terms of the free space wavelength.

All I’ve gotten so far is:
E(y,t)=E0cos(kyy\u2212wt)
\u03bb=2\u03c0ky
I don’t know how to determine ky or k\u00af. I’m basically totally stumped on this problem. Of course it needs to be in terms of:
\u03bb0=2\u03c0c\u03c90<\/p>\n\n\n\n

Quiz 12.<\/strong><\/p>\n\n\n\n

Lagrangian of a mass between two springs with a pendulum hanging down<\/h6>\n\n\n\n
Homework Statement:<\/h6>\n\n\n\n

A particle of mass m1 hangs from a rod of negligible mass and length l, whose support point consists of another particle of mass m2 that moves horizontally subject to two springs of constant k each one. Find the equations of motion for this system.<\/p>\n\n\n\n

Relevant Equations:<\/h6>\n\n\n\n

L=T\u2212V<\/p>\n\n\n\n


What I first did was setting the reference system on the left corner. Then, I said that the position of the mass m2 is x2. I also supposed that the pendulum makes an angle \u03b8 with respect to the vertical axis y. So the generalized coordinates of the system would be x2 and \u03b8. Thus, the coordinates of m1 are:

<\/p>\n\n\n\n