Homework Statement
A bar suspended in air weighs 1.75 N
The same bar weigs only 1.4 N when suspended in water.
Calculate;
a. upthrust
b. density of the bar
Homework Equations
D = m/v
F = m*a
The Attempt at a Solution
a[/B].
Upthrust is 1.75 N - 1.4 N = 0.35 N
b.
Assuming density of water...
I found what was called a "dichromatic prism" on ebay and bought it. It is a cube and although described as "not perfect" it splits light extremely well and is quite a cool object to show those in my staff room.
I understand that dichroic is different but not sure how.
Question is, how does it...
Homework Statement
A cylinder of radius a and length l has charge distribution
ρ=Cr2
where C is a constant and r is radial distance in cylindrical coordinates.
Derive an expression for the average charge density within the cylinder.
Homework Equations
Well, charge density given is within the...
I have looked at the question and unscrewed the bits of paper I attempted my answers on and the h0 seems to be a complete typo, it all says just plain h. I will try to work through with that in mind, as you say.
Homework Statement
Find magnitude of net upward force on a cube in terms of l, ρ (rho), g and h. then show that h = m/ρl2
A solid cube, mass m, side length l, is placed in a liquid of uniform density, ρ(rho), at a depth h0 below the surface of the liquid, which is open to the air.
The upper...
Homework Statement
A solid cube, mass m, side length l, is placed in a liquid of uniform density, ρ(rho), at a depth h0 below the surface of the liquid, which is open to the air.
The upper and lower faces of the cube are horizontal.
Find the magnitude of force, Fs, exerted on each vertical...
Having been a junior design engineer 15 years ago and moved out of that field I am looking to get back into a science based career.
I am taking a "Natural Science" degree with a maths/physics bias (lots of that) and can't seem to get any sensible job before I get this in place.
I used to use...
I recently watched a documentary presented by Professor Brian Cox called Human Universe.
In it he was wondering how much leeway he would have, if he was "the creator of our universe", to alter the physical constants.
He then went on to say that if he altered the speed of light one way then...
I have a difference of opinion with 2 calculation engines.
equation to solve is;
d/dx (a(x^2 +y)
Wolframalpha of course is a very trusted source but I also use symbolab.
Here is a screenshot of the differential I want from both sites and associated answers.
. . . and the wolfram solution...
Sorry, I should have said.
D1 ┴ is the electric displacement in media 1 perpendicular to a boundary with a different media
D2 ┴ is the electric displacement in media 1 perpendicular to a boundary with a different media
They form the boundary condition
could have been
D1 = D2.
and P is the...
Homework Statement
a parallel plate capacitor has 2 plates separated by a dielectric of rel. permittivity 5.0 are separated by 0.20mm and have area of 5.0 cm2.
Potential difference between the plates is 500V.
I need to be able to calculate the free surface charge density...
A problem involving E, D & P. I have the answer but not sure why for the P bit.A bit of clarification if someone could, please.
A thick sheet of polystyrene, of relative permittivity ε = 2.5, is placed
normal to a uniform electric field of magnitude 500Vm−1 in air.
Find the magnitudes of...
Homework Statement
A thick-walled cylindrical tube of dielectric material has internal radius a/2 and external radius 2a, and its polarization is given in cylindrical coordinates by the expression P = (A/r2) er.
Derive expressions for the net charge on the inner and outer surfaces of a...
Homework Statement
Glass has a permeability of ε=2.0 and relative permeability μ=1.
Electromagnetic radiation of angular frequency ω=2.8x109 s-1. travels through the glass. Calculate
a) refractive index
b) speed of radiation
c) frequency of radiation
d) wavenumber of radiation
a, b...
Homework Statement
Still having a little trouble so here's the problem.
(ex + ez) x (3ey - 4ez)
The Attempt at a Solution
(ex * ez) + (ex * (-4ez)) + (ez * 3ey) + ( ez * (-4ez)
now, these are all orthogonal to each other, so, for example, if I have ex * ey then I should end up...
Homework Statement
A current element is 3.0mm long, centerd on the origin of cartesian coordinates, and carries a current of 2.5A in the direction ez.
What field does it produce at the point (3.0, 0, 4.0)
Homework Equations
This is obviously a Lorentz force law question
so . . . ∂B =...
As I understand, when an electric field is applied to an atom then the nucleus and electron cloud will be shifted out of balance giving rise to an electric dipole moment. Some molecules have permanent dipole moments though,
e.g. Hydrogen Chloride,
". . . when a hydrogen chloride molecule is...
Homework Statement
Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0)
+q1 at x = 0
-q2 at dist from origin x = a
+q3 at dist from origin x = -2a
where q1, q2 and q3 are magnitudes of the charges.
Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on...
I understand that the sun changes magnetic polarity far more often than Earth does (correct me if I'm wrong as it's just what I read).
Apparently it is statistically likely that the Earth's magnetic field will change polarity at some time, so what sort of effects will this have in practcal...
Hi.
When I point my red laser pointer at the playable side of a CD at an angle the spot becomes diffracted, a bit like the fringes you can get if you put a hair across the beam.
Could you keep to the CD phenomenon, when trying to explain and whether it really is related to Youngs Fringes or...
Ah!
n = principal quantum number
m = mass of electron
L2 = square of magnitude of orbital ang momentum.
so . . . .
E = 22 ∏2 hbar2 / 2(9.1x10-31) 2 hbar2
E = -2∏hbar/m
er! surely too messy and probably wrong.
Hmmm!
Well, En = (n + 1/2) hbar ω0
and
En = n2 ∏2 hbar2 / 2mL2
where principal quantum number n = 0, 1, 2 . . .
but I can't evaluate ω0 and I don't have the mass for the other one . . do I?
Homework Statement
Hi, my question is regardng a Coulomb model of an H atom specified with Hamiltonian operator, Hhat, by spherical coordinates of energy eigenfunction
ψ2,1,-1 (r,θ, ∅) =(1/ 64∏a02)1/2 r/a0 e-r/2a0 sinθ e-iθ
Principal quantum numer n = 2
orbital an mom l = 1
magnetic...
I have a pair of non interacting, identical 1/2 spin fermions in a one dimensional infinite square well with walls at x=0 and x=L.
One particle is in ground state, the other in first excited state.
This two-particle system has total spin quantum number S=0
I have normalized energy...
OK. An example I have has me stumped temporarily. I'm tired.
General spin matrix can be written as
Sn(hat) = hbar/2 [cosθ e-i∅sinθ]
...... [[ei∅sinθ cosθ]
giving 2 eigenvectors (note these are column matrices)
I up arrow > = [cos (θ/2)]
.....[ei∅sin(θ/2)]
Idown arrow> =...
Homework Statement
I have a similar problem to this one on Physicsforum from a few years ago.
Homework Equations
Cleggy has finished part a) saying he gets the answer as
Ψ(x, t) = (1/√2) (ψ1(x)exp(-3iwt/2+ iψ3(x)exp(-7iwt/2)
OK
classical angular frequency ω0 = √C/m for period of...
Homework Statement
.
Hi, could someone look at the attachment & comment on whether I'm anywhere near getting the expectation value correct, please.
In the grnd state;
1. terms such as AA†A†A, with lowering operator on RHS has zero expectation value,
2. terms such as AA†A†A† with uneven...
I realize that at ground state of a harmonic oscillator the energy will be at zero.
I'm assuming that the expectation value will also be at zero.
Could someone confirm this & possibly explain just a little more.
Thank you
A little behind in this subject, but I understand raising & lowering operators to almost be factors of the Hamiltonian operator.
raising - Ahat dagger = 1/√2 (x/a - a*(δ/δx))
lowering - Ahat = 1/√2 (x/a + a*(δ/δx))
I also have the Hamiltonian as;
Hhat = (Ahat dagger * Ahat + 1/2)...
Homework Statement
I'm asked to start from Faradays Law & Ampere-Maxwell law then derive the equation for the magnetic field, B, in the form;
del2B = 1/c2 * d2B/dt2
Homework Equations
Faraday: curl E = -dB/dt
A.M : curl B = ε0μ0 dE/dt
The Attempt at a Solution
taking curl of...
When an EM wave encounters a dielectric some of the wave is transmitted & some reflected, as with a metal, too.
When encountering a metal the normal part of the EM wave will absorb a small amount of energy, up to the skin depth, but a dielectric will allow the normal incidence of the wave...
Facets of a rock specimen sparkle brightly
In terms of electromagnetism how can I show that a linearly polarised light source can be used to determine that the facets are dielectric rather than metallic?
Should have to do with scattering, but not sure whether it could be explained with a...
Homework Statement
A parallel plate capacitor with plates of area, A & separation of d is filled with LIH dielectric of relative permittivity ε. By considering energy associated with the electric field derive an expression for electric energy stored in the capacitance when a voltage of V is...
OK, OK I've kicked off a bit early.
I will be using the equations booklet & make sure I look at it to complete problems in the way I've been taught (although coming back to it from a while ago dulls the mind if you're not using it).
1. divergence should be proportional to the density of magnetic "charge" (div B = 0 - no monople law)
2. div E = ρ / E0
(and for a conservative (electrostatic) field the curl should be zero. (Faradays law - curl E - -∂B/∂t))
The difference is that I "get" 2 and can show this by the matrix I...
Homework Statement
Three vector fields are listed below. Determine whether each of them is electrostatic field or magnetic field.
Homework Equations
F1(x, y, z) = A (9yz ex + xz ey + xy ez)
F2(r,∅,z) = A [(cosx/r)er + (sinx/r) e∅]
F3(r,θ,∅) = Ar2 e(-r/a) er
The Attempt at a Solution
Used...
Homework Statement
A long straight wire carries a current of 2.0A. An electron moves parallel to it at a distance of 0.01m (I'm assuming id doesn't matter which way it moves) at a velocity, v = 100ms-1
Calculate magnitude & direction of force acting on it.
Homework Equations
B = μ0 L / 2∏r
F...