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seen Apr 5 at 15:56

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awarded  Popular Question
Mar
20
asked Fugacity of the fermi gas
Mar
17
comment Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$
If $R_{21}$ is an eigenfunction of $L_z$ then all measurements of this quantity when the wavefunction is in such a state will yield the same value always. So, in that case, the answers to a) and b) will be the same. I am currently learning QM as well so someone correct me if this is incorrect. Your wavefunction is conveniently expressed in terms of the eigenstates of both $L^2$ and $L_z$ so by acting with these operators onto the eigenstates gives the possible values immediately.
Feb
2
comment Some subtleties in direction of drag force
I find it easier to use vectors; what would the corresponding vector equation be for the scalar equation $F = -mg -\mu v$? If $\hat{x}$ is upwards then there should be a term like $-mg\hat{x}$. And since $\mathbf{F_{drag}} = -\mu \mathbf{v} = -\mu v (-\hat{x}) = + \mu v \hat{x}$
Feb
2
comment Some subtleties in direction of drag force
But the drag term should not be pointing down - the body is moving downwards and so drag should point upwards. (This has to be the case otherwise a terminal velocity could not exist since both forces would be acting in same direction). $\mathbf{F_d} = -\mu \mathbf{v}$ and $\mathbf{v}$ is downwards, so $\mathbf{F_d}$ is upwards.
Feb
2
awarded  Commentator
Feb
2
comment Some subtleties in direction of drag force
Thank you, that does indeed fix the problem. However, I do not see the reasoning behind Morin's equation (P.63 if you have access) $F = -mg - \mu v$ This implies both forces act downwards (since he assigned +ve $x$ upwards).
Feb
2
asked Some subtleties in direction of drag force
Nov
14
asked Properties of material affecting magnetic refrigeration
Nov
13
comment Understanding the Ampere's Law
Since $P$ is equidistant from both wires and the currents in the wires are in opposite directions, then the result you have $|\mathbf{B}| = \frac{\mu_O}{2 \pi r} \left(I_1 + I_2\right)$ is correct. The orientation of $L_3$ is a bad choice of amperian loop because it does not exploit the symmetry of the $B$ field.
Nov
13
asked Transitions in a magnetic refrigeration
May
13
awarded  Scholar
May
13
comment Charge inside conductor
Okay, many thanks again
May
13
accepted Charge inside conductor
May
13
comment Charge inside conductor
You said above 'assuming not a hollow sphere'. How would this change things?
May
13
comment Charge inside conductor
That's a nice answer - thank you. So the charge located inside will redistribute (evenly) over the surface of the spherical conductor. And then we conclude no charge so no field?
May
13
asked Charge inside conductor
May
1
comment Importance of Ampere's Law
Yes, that is my confusion. Considering the B field from the inner cylinder first yields a non zero B field. However, the Amperian loop I used to deduce this does not 'shield' the B field from the wire. So even though I used the Amperian loop to deduce a non zero field, in reality there is also the field from this wire.
May
1
comment Importance of Ampere's Law
Actually, I think I didn't make myself very clear in my second comment above. Enclose the solid cylinder within the hollow cylinder. Then at some P < b, the B field is only due to the solid cylinder and is nonzero. Let's say I then have a wire outside the hollow cylinder such that the B field it produces is directly opposite the direction of the B field due to the solid cylinder at P. So the net B field is zero (at P) yet by Ampere, we attain a non zero B field. What is wrong with this analysis?
May
1
comment Importance of Ampere's Law
So as my example illustrates, it really only gives you the B field if the problem is highly symmetric and it only really helps in giving the B field locally? (What I mean by this is that even though the Amperian loop within the hollow cylinder gives a zero B field from the cylinder it tells us NOTHING about the B field from the wire - so even though we enclose a certain region within an Amperian loop and the B field happens to be zero for one source, we cannot conclude that the B field is entirely zero). Do you have any thoughts about my second comment posted above? Thank you.