Zero Definition and 1000 Threads

Homework Statement Which one of the following statements concerning electrostatic situations is false? a) No work is required to move a charge along an equipotential surface. b) If the electric potential with a region of space is zero volts, the electric field within that region must also be...

Is there a good general definition of 0^z, where z may be complex? The cases where z is real (and positive, negative, or zero) are straightforward, but what if z isn't real? Are there arbitrary branch cuts involved, or is there some universal definition?

Lets say H = [3a+b, 4, a-5b] where a and b are any scalars. This not a vector space because Zero vector is not in H. I don't get what it means by zero vector is not in H? Can't you just multiply the vectors by zero and get a zero vector? I am confused.

Is zero a real number?

Hi, I have read Steinmetz books and he has a very good example of OC phenomenon that is nothing like AC case. There are certain conditions under which an OC transformer has zero impedance. Also, on his chapter of long transmission lines, he says quarter wave resonance using abrupt pulses can...

Can something even exist without energy? And if it can will it truly not move?To be clear I know E=mc2 but can something exist without any movement?

I tried to prove this claim, as I require it to finish one of my proofs. By definition, if a,b are integers, with a \ne 0, we say that a divides b if there exists an integer c such that b = ca. So, n divides 0 means that there exists some integer c such that n = c*0 = 0. But this would...

Homework Statement This problem is found in a chapter about rational functions in my review book. The expression is as follows: \lim_{x\rightarrow a} {\frac{2 x^2 + 5x - 3}{x - a}} = \ \text{L} where 'a' is a constant. I'm supposed to find a value of 'a' that allows the limit to...

I am talking about electromagnetism.. Can we construct a system with no power consumption.. I ve an idea... 1 we can construct rail route surrounded by dome shaped copper (actually cu strips to avoid eddy current) 2 rail on which permanent magnet is fixed will allowed to move on this...

Consider an adiabatic expansion of an ideal gas that work is done against friction or a piston. Since no heat exchange can occur the gas keep on losing energy and its temperature decreases and the gas molecules getting further and further apart. In principle the temperature can get down to a few...

We know that a null vector (or zero vector) has direction but no magnitude. I am having some trouble understanding this concept. 1. What's the direction of a null vector, really? 2. Also as null vector is a vector, can velocity or acceleration also be null vectors? 3. If so, then what...

I'm supposed to find the gradient vector of the function below at (0,0), and then use the dot product with the unit vector to find the directional derivative. Then find the directional derivative using the limit definition of a directional derivative, and explain why I get two different...

Hello Here is an example.we want to calculate value of x where Electric filed going to be zero.i want to use vector form of coulomb equation So as we know for 1c: for -9C: so as we do superposition we obtain So In this problem x doesn't have any real number.what is my problem? Any help...

I'm studying magnetic properties of nanoparticles in a liquid carrier and trying to understand better zero-field-cooled/field-cooled curves. We use the Stoner–Wohlfarth model and Chantrell calculations to model ZFC/FC curves but I'm having some issues to follow the calculation. Does anyone...

please go to "Wolfram Alpha" website, (google the term) and copy paste the following formula: curl ( (-y/(x^2+y^2), x/(x^2+y^2), 0) you can see the result is zero I think that's the expression of H surrounding a current. what am I missing?

calculate the Fourier transform of the function g(x) if g(x) = 0 for x<0 and g(x) = ##e^{-x}## otherwise. putting g(x) into the transform we have: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-ipx} e^{-x} dx## which we can write: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-x(ip+1)} dx##...

hey pf! when would you use "identically zero" as opposed to simple "zero". example: f is identically zero on interval a to b. or, f is zero on interval a to b. why do we ever use identically? it seems superfluous... thanks!

Homework Statement Part (a):Find the first order shift in energy Part(b): What is the degeneracy after perturbation? Find Show average shift in energy is zero. Homework Equations The Attempt at a Solution I've shown part (a), the troubling part is part (b). Part (b) With the perturbation...

No heat exchange is facilitated during an adiabatic process. Change is heat is zero. How does this relates to the entropy being zero? ∫dQ/T? But this could really just mean that the integral is of any constant.

There are two charges 2 C and 3 C and 100 cm apart from each other. Find a point where electric potential is zero? Consider 2 C charge on the origin.I have tried out but don't get it solution... 1) If you take point between two charges then 2 C----------100 cm------------------3 C...

Hi, I am having trouble understanding why Tij can be non-zero for i≠j. Tij is the flux of the i-th component of momentum across a surface of constant xj. Isn't the i-th component of momentum tangent to the surface of constant xj and therefore its flux across that surface zero? What am I...

1.)Two charges are fixed in location: charge q1= +8e is located at the origin and charge q2= -2e is located on the x-axis at x=L. At what point can a proton be placed so that it has net zero force acting on it? 2.)F=kq1q2/r^2 3.)I tried to do F=0 K = 8.988 X 10^9 (constant) q1 = (8...

w = ΔKE + ΔPE For a particle moving at constant speed, there is no change in velocity so no change in KE. What about change in PE for a partcile moving at constant speed on a equipotential surface? Would I be right in stating that since the particle moves along the same surface (AKA same...

Homework Statement I have solved the equation $$x^3=7x^2$$ giving roots at $$x=7, x=0$$ The solutions in the book also give a specific third solution of $$x=0$$ again. I can't see the point of this unless it is to reassure the reader that there are no further solutions to look for given...

Hello, I watched a lecture by Leonard Susskind, in which he said that a differential is so short that when you square it, you get zero. What exactly could he mean by this? Thank you for your time. Kind regards, Marius

Homework Statement Let ##A\subset E^n## and let ##f:A\to E^m.## Consider the condition that there exist some ##M\in\mathbb{R}## such that ##d(f(x),f(y))\le Md(x,y)## for all ##x,y\in A.## Show that if the condition is satisfied, if ##m=n##, and ##\text{vol}(A)=0##, then...

Homework Statement Find the zero input and zero state response for the following system y''(t) + 3y'(t) + 2y(t) = 2 x'(t) - x(t-1) where x(t) = (2e^-t)*u(t) U(t) is the step function Homework Equations Y = Yh + Yp Y = Yzsr + Yzir The Attempt at a Solution I can't find...

1. A link is connected by two bearings A and B. The bearings run along slots which are at right angles to each other. The length of the link AB (length between the centres of bearings A and B) is 0.2m. At an instant of time, height H, is 0.05m, and the bearing A has a constant velocity V, of...

Hello, this isn't a homework problem, so I'm hoping it's okay to post here. I would like to know the correct way to mathematically express the idea in my title. It is intuitively obvious that as the radius of a circle increases, it's curvature decreases. I looked it up and found that...

That 2 terminals shows PD of 1 volt on Meter, but when shorted, there is no current shown on Meter? I checked and rechecked [using different meters, wires, AC, DC options and what not], so I see only V measurement, but no I. Is it possible? If so, then what is the use of that PD, when we can't...

Homework Statement Let us have a square ABCD (D is in the topleft corner) of size 1 m. Let us have 3 point charges situated in points B, C and D. The charges are following QB=2C, QC=-1C and QD=5C. The task is to find (a) the points/plane where the electric potential is zero and (b) two points...

Homework Statement (a) Let \alpha:I=[a,b]→R^2 be a differentiable curve. Assume the parametrization is arc length. Show that for s_{1},s_{2}\in I, |\alpha(s_{1})-\alpha(s_{2})|≤|s_{1}-s_{2}| holds. (b) Use the previous part to show that given \epsilon >0 there are finitely many two...

If you have an augmented matrix and one column in your matrix is all zero (but not the answer column) are you able to 'delete' the all zero column and the corresponding variable? Because when you write out the equations, the co-efficient's of the variable corresponding to the all zero column are...

Hello! :D I am given the following exercise:Find all the zero divisors in the ring $\mathbb{Z}_{20}$. For each zero divisor $[a]$,find an element $[b] \neq [0]$ such that $[a][b]=[0]$. That's what I did..Could you tell me if it is right?? Zero divisors at the ring $\mathbb{Z}_{20}$: $\{ [2]...

P.W. Anderson in his essay "more is different" said that: "no stationary state of a system has an electric dipole moment". He used an example of NH3 to illustrate that. I then checked online and found that, Chemists said there is dipole moment in NH3 molecule, but (nuclear) physicists claim...

Hey! :o An infinite orthonormal system $\{e_1, e_2, ... \} \subset H$ is closed in $H$ iff $\forall x \in H$ $$||x||^2=\sum_{i=1}^{n}{|(x,e_i)|^2}$$ From the summability of the right part of the relation above, we conclude to that the sequence $(x,e_i)$ is a zero sequence. Could you explain...

Hi guys, I am having trouble showing that \mathbb{E}\left[(Y-\mathbb{E}[Y|X])^{2}\right]=0. I understand the proof of why E[Y|X] minimizes the mean square error, but I cannot understand why it is then equal to zero. I tried multiplying out the square to get...

Most graphs show that when wheel slip is zero then the friction is zero. But I can't get it, as when the vehicle stand still on slope, the friction keeps the vehicle from going down hill Could someone explain for me? http://www.albi-engineering.nl/Electronics/Traction_Control/slipgraph.jpg

For the following algebraic expressions for the Laplace transform of a signal, determine the number of zeros located in the finite \(s-\)plane and the number of zeros located at infinity. Does that mean pole since at a pole the plot will diverge to \(\infty\)? Otherwise, what would be a zero...

Given the stress tensor in a point, determine the zero normal stress plane. ...2 3 0 T= 3 2 0 ...0 0 5 ---------------------- Eigenvalues: σ1=σ2=5, σ3=-1 It must be simple, but I don't know how to determine the normal vector of that plane analytically. I know σ=0. t=Tn=σ+τ=τ If normal stress...

Homework Statement Two point charges are placed 1.00m apart. q(1) = -2.50 x 10^(-6) C q(2) = +6.00 x 10^(-6) C Task is to find where along the line, other than at infinity, the electric field will be equal to zero. Homework Equations E = (k * q) / r^2 The Attempt at a Solution...

Suppose you have a system of charges on the xy plane. Am i correct in saying that the place where you have zero volts, is the place where you can put a charge and it WONT move?

I just performed a lab in my physics class, and there are a few conceptual questions that I am having trouble with. The lab was simple. We took a constant volume sphere made of Stainless steel and filled with air. We changed the temperature of the water it was into record the corresponding...

Homework Statement Two point charges are placed on the x axis. The charge + 5 q is at x =1.50m , and the charge −q is at x= -1.50m . There is a point on the x-axis between the two charges where the electric potential is zero. Where is this point? The electric potential also vanishes...

Hi, I am fairly new to superconductivity (introductory college level). I have covered and grasped the basics but was wondering if someone could shed some light on what specifically causes materials to have zero resistance when they become superconducting. I know that cooper pairs form when the...

It is given that $a_{n}$ is a positive and decreasing sequence. Show that if $\sum_{n=1}^{\infty}a_{n}$ converges, $\lim_{n \to \infty}na_{n}=0$. That's what I tried.Could you tell me if it is right?? $\sum_{n=1}^{\infty}a_{n}$ converges,so it satisfies the Cauchy criterion,so : $\forall m,n$...

Homework Statement Consider a solid conducting sphere with a radius a and charge Q1 on it. There is a conducting spherical shell concentric to the sphere. The shell has an inner radius b > a, outer radius c and a net charge Q2 on the shell. Denote the charge on the inner surface of the shell...

Suppose that operators A and B have complete sets of eigenfunctions, [A, B] = 0, and Ψ is an eigenfunction of A with the eigenvalue a, namely AΨ=aΨ. Then we have A(BΨ) = BAΨ = a (BΨ). They say (BΨ) is also the eigenfunction of A. Why? How do we know (BΨ) is not equal to zero?

Hi, apologies if this is simple. I'm a bit confused with a piece of text from Introductory Nuclear Physics by Wong. It's talking about finding the expectation value of the magnetic moment of the deuteron. In the deuteron it is known the total spin quantum number is S = 1. In deriving the total...

Homework Statement Show that \left(\frac{\partial H}{\partial T}\right)_{T} = 0 for an ideal gas Homework Equations The question required me to first solve \left(\frac{\partial U}{\partial T}\right)_{P}...