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Hi, thanks for this! How would I proceed in measuring the inductance using frequency domain reflectometry? I understand that one-way would be to basically build an LCR series circuit with proper impedance matching with respect to the source transmission line and to measure the reflectance at the...

Hi all, I recently fabricated a bunch of gold coils patterned onto a glass substrate and am in need of measuring the inductance of these samples. Since the feature size is in microns, I can't exactly use an RLC meter. At the moment, I'm trying to build an LCR series circuit with a PCB and...

Hi everyone, I've been studying about semiconductor heterostructures and in particular quantum dots. I was wondering, why is there a need to have a "capping" layer above the layer where the quantum dots are formed within a sample? Thanks in advance!

Now from the relevant equations, $$U(t) = \exp(-i \omega \sigma_1 t)$$ which is easy to compute provided the Hamiltonian is diagonalized. Writing ##\sigma_1## in its eigenbasis, we get $$\sigma_1 = \begin{pmatrix} 1 & 0\\ 0 & -1\\ \end{pmatrix} $$ and hence the unitary ##U(t)## becomes...

Hi! Reading through this paper, the Hall resistivity in ferromagnetic materials is given by $$\rho_H = R_0 B + 4 \pi R_s M$$ It is mentioned that ##R_s## (anomalous Hall coefficient) is significantly larger than ##R_0## (ordinary Hall coefficient) and has a strong dependence on temperature...

Hi! I'm trying to understand the dependence of spin hall voltage on various parameters of the material. I have been going through this paper, and it is mentioned that $$V_{SH} = 2 \pi R_s L j_x n \mu_B$$ In the equation, only ##L## and ##j_x## seem to be the variables. Does increasing ##L##...

@Choppy, Thanks a lot! This is very insightful. I'll try to keep these in mind. :-)

@hutchphd, thanks a lot! My semester is ongoing at the moment and I'm so overwhelmed with all of this. Hopefully, things will get better with time. Stay safe. :-)

Hi everyone! Hope you all are doing well in these tough times. Currently my country is going through one of the toughest second waves of Covid and frankly seeing the news is terrifying to say the least. Being at home, I've noticed that I haven't been able to study for a significant period of...

This is my reference circuit. This clearly produces the state ##\frac{1}{\sqrt{2}}(|01\rangle + |10\rangle)##. This is obviously until the measurement is done. However, I'm trying to implement a circuit which essentially gives me a 50-50 chance of getting either ##|01\rangle## or...

Thanks but I'm asking if some circuit components can be added somehow to process the former state to be the final state in question.

Hello everyone! I'm trying to implement a quantum circuit that yields a superposition state $$\frac{1}{\sqrt{2}} (|01 \rangle + |10 \rangle)$$ I'm using parameterized gates to achieve this. I have been able to create the state $$\frac{1}{\sqrt{2}}(|01\rangle + e^{i\phi} |10 \rangle)$$ Is there...

I'm not familiar with the latter one.

I'm sorry for not mentioning but the rolled paper tube is placed vertically on a flat surface and left to unwind.

I came across a problem regarding a paper being rolled into a tube. When a piece of paper is rolled into a tube and then left to unwind, it is always seen that the unwinding happens in jerks and not smoothly. Why is it so? What I have thought (and thanks to some discussions on reddit), that...

I am currently doing a research project on the topic "Anisotropic magnetoresistance" for which I have referrred various textbooks. All the textbooks state that for this phenomenon to be observed, it is necessary for the object to have more than one carrier type. This has been explained...

Thanks for the insight :)

There's this problem 2.18 in the book "Introduction to electrodynamics" by Griffith. The problem says the following, "Two spheres, each of radius R and carrying uniform charge densities ##+\rho## and ##-\rho##, respectively, are placed so that they partially overlap (Image_01). Call the vector...

Please show an attempt that you made at solving the problem.

Make sure that you understand linear momentum conservation properly and come back to the question after thoroughly understanding the concept :)

Yeah, I got it. Thanks

Let a function ##f:X \to X## be defined. Let A and B be sets such that ##A \subseteq X## and ##B \subseteq X##. Then which of the following are correct ? a) ##f(A \cup B) = f(A) \cup f(B)## b) ##f(A \cap B) = f(A) \cap f(B)## c) ##f^{-1}(A \cup B) = f^{-1}(A) \cup f^{-1}(B)## d) ##f^{-1}(A \cap...

The power ratings of bulbs come along with a voltage value. For example a bulb with rating 1000W,40V means that when 40V is supplied to the bulb, its power consumption will be 1000W. Now ponder over this and you should arrive at the answer.

Let me start from scratch. Case 1: I resolve normal reaction vector as one along y-axis as ##Nsin\theta=mg## Case 2: I resolve ##mg## along the surface of cone and perpendicular to the surface as ##mgsin\theta=N## Now by your previous statement both the methods are correct however we end up with...

Let's say the problem was to find the magnitude of normal reaction acting on the body. Clearly both the values of normal can't be the same (refer 2nd image). Then what's the right value of the normal reaction ?

Thanks but another doubt arises in my mind. When am I supposed to consider centripetal acceleration (towards the centre of trajectory) and centrifugal acceleration (away from centre) ?

Also if any of the vectors can be resolved then when resolving acceleration and mg in the direction perpendicular to the surface and along it then we get... (refer image). However the body doesn't move along the surface but through this approach a net force appears. Where am I going wrong?

What's wrong in this approach ? (refer the image provided)

I'm apologize for my ignorance. I've made the required change.

Homework Statement Refer the given image. [Prob 2.9] Homework Equations F=ma The Attempt at a Solution I drew the normal vector perpendicular to the surface of the cone and resolved it as ##Nsin\theta=mg## ##Ncos\theta=\frac {mv_{0}^2} {r}## where ##v_{0}## and ##r## are the speed and radius...

Thanks I got it.

Well the answer is 3240

Homework Statement Refer the image Homework Equations Equations for permutations and combinations The Attempt at a Solution Let x be the no. of questions that turned out to be correct. So total score will be 3x-(10-x)=4x-10. The value of this expression must be from the given set and since x...

It's from an exam paper called NEST (National Entrance Screening Test) conducted in India. Its for the year 2016.

I'm sorry but I don't quite understand. The answers given are b,c,d.

Homework Statement Refer the image. Homework Equations kq1q2/r^2 = F Potential energy = kq1q1/r The Attempt at a Solution Obviously since both charges are unequal in magnitude option a is incorrect. Calculating field at large distance r, E = kq1/r^2 - kq2/r^2 = kq2/r^2 Also potential energy...

Then from there on how do I proceed? Options B and C get ruled out.

##a=\frac{e-1} {\int_0^1 e^{x^2}\,dx}## And from the above quoted equation, ##a=\frac{e-1} {<e-1}## Hence ##a>1##. Is this correct?

So that ##\int_0^1 e^{x^2}\,dx## and ##\int_0^1 e^x\,dx## can be compared. Clearly ##\int_0^1 e^{x^2}\,dx## < ##\int_0^1 e^x\,dx##

Homework Statement Refer the image. Homework Equations Integral (e^x)dx from 0 to 1=e-1. The Attempt at a Solution Refer the other image. The graph of e^(x^2) increases more slowly than e^x till x=1. So 'a' is clearly greater than 1. Is this right?

Solution set includes (0,0,0) , (1,2,2), (2,4,4) and so on. This then gives a straight line. Thanks :bow:

I compared the real and imaginary parts separately and ended up with the relation a=2b=2c.

Homework Statement Refer given image. Homework Equations Expansion of determinant. w^2+w+1=0 where w is cube root of 1. The Attempt at a Solution Expanding the determinant I got cw^2+bw+a-c=0. Well after that I have no idea how to proceed.

So compression is maximum when both masses have equal velocities.

If mass m moves by x1 wrt mass M and mass M moves by x2 wrt ground then spring compression will be x1-x2.

I think when mass m stops moving relative to the ground is when max compression occurs.

Homework Statement The attached image. Homework Equations Momentum conservation Conservation of mechanical energy The Attempt at a Solution I tried conserving momentum, ##P=mv_{1} + Mv_{2}## and then conserving M.E., P^2/(2m)=1/2##mv_1{1}^2## + 1/2##Mv_{2}^2## After that I can't seem to...

Ok, thanks a lot.

I think I'm a bit hazy about it.

Lets put it this way, obviously current flows in the circuit and till that time there is a varying electric field inside the capacitor. Now I am not sure why does the flow of current stop when the electric field becomes constant inside the capacitor.