1. Det of Triangular-like Matrix & getting stuck in Algorithmic Proof

Find determinant of following matrix: ## A = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n-1} & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n-1} & 0 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ a_{n,1} & 0 & \cdots & 0 & 0 \end{pmatrix} ## Note: I tried to solve this question...
2. Help please solving this electromagnetism problem -- coil moving near a magnet

A small coil is moved forward (without turning) between the poles of the electromagnet. Does an electric current develop in the coil? Explain the answer
3. Motion-powered GPS tracker to install permanently inside a bicycle frame

Briefly, the problem; stolen bicycles are notoriously difficult to recover. Designing a GPS tracker to fit on one is challenging, because bicycles rarely have their own available power source. Whatever GPS unit is used must typically have its own battery as its sole source of power, which...
4. I Electrostatic induction - how to quantify it with a theoretic integral or similar

Assume that a certain charge distribution ##\rho## generates an electrical field ##E_{ext}## in the surrounding space. We also note the corresponding generated potential ##V_{ext}##. Assume furthermore that a conductor A, with a definite shape and volume, is placed in field ##E_{ext}##, and is...
5. Electromagnetic Induction of a Disk

Hello I'm having trouble finding the right way to apply Faraday's law to this question. I've found the flux through the disc: ##\phi = \vec A \cdot \vec B = B_{0} \sin{\omega t} \left( \frac D 2 \right)^2 \pi ## and the EMF: ##\varepsilon = - \frac {d \phi} {dt} = -B_{0} \omega \cos{\omega t}...
6. Simple Induction Help with Lemma for proof of AM-GM inequality

Summary:: x Hey, I'm learning calculus and had to prove the following Lemma which is used to prove AM-GM inequality, I had tried to prove it on my own and it is quite different from what is written in my lecture notes. I have a feeling that my proof of the Lemma is incorrect, but I just don't...
7. Simple Induction Direct Proofs regarding Induction

Summary:: . When asked to prove by Induction, i'm asked to prove a statement of the form: Prove that for all natural numbers ##n##, ## P(n) ## Which means to prove: ## \forall n ( P(n) ) ## ( suppose the universe of discourse is all the natural numbers ) Then, I see people translating...
8. Eddy currents in Faraday's Law Experiment

My explanation: A circular coil is connected to an AC supply at a frequency of 30-50 kHz (radio frequency). Therefore, an alternate current will be running through this “primary” coil, producing an alternating magnetic field. This magnetic field periodically decreases in strength, alternating...

10. Conservation of energy when placing two inductors next to each other

This is more like a theoretical question of my own than actual homework. Say there is a circuit with a current source and an inductor. There is a current ##i(t)=at## going through the inductor. We now place a new circuit with an inductor and a resistor next to it. The current ##i(t)## causes a...
11. Find the speed of a copper loop falling in a magnetic field

Hi all, so I had this problem and on the exam and I got a solution but I had an mass-term in there which wasn't given. I used Farraday's Law of Induction to get the Voltage induced. Then I used ##rho* \frac{A}{4a} ## for the resistance and divided the Voltage by that to get the current. I then...
12. 50Hz 3 Phase Circuit - Twisting to reduce EMI?

I have done the maths to work out the Induced Voltage on a communication cable, from a bunch of 3 phase circuits in a panel - with the minimum distance between them I calculated it to be about 1.5nV; but for a larger system where there could be larger loads on the cables I was thinking about...
13. Force on a copper loop entering into a magnetic Field B with speed v

Hi, second problem in one evening, I'm sorry! But i'm also not quite sure if I did this one right. I had thought I need lenz's law but there is no current before entering the field so I just use the induced Voltage? My approach: ## V = \frac {B*A}{t} ## ## IR = \frac {B*A}{t} ## and ## A = v*t...
14. How to calculate the voltage induced in a coil by an AC magnetic field?

So, as it says in the title, I am trying to calculate overall voltage induced in a coreless coil in the cases of it being stationary and moving in an alternating magnetic field. To go more into detail, I would like to create a mathematical model of a coil in an alternating magnetic field that...
15. Prove the decomposition of a graph w/ even edges produce a 2-path set

For my base case I just used a graph with three vertices and 2 edges. Decomposing this would just give us the same graph, which has a path length of 2. The inductive step is where I'm having some trouble: One idea I have is that we take a graph G then inductively remove an edge to create two...
16. Proof by Induction: Arithmetic Sum

Hi, I am self studying induction and came across the following problem. I am stuck on how to proceed (I need to use induction, I know there is a direct proof). My proof attempt is as follows: Let ## P (m) ## be the proposition that: $$\sum_{i = m + 1}^{n} i = \frac{(n - m)(n + m + 1)}{2}$$...
17. Interesting Magnetic Field Induction Problem

Homework Statement Suppose we have an isolated, long, narrow straight wire with low electrical resistivity. A constant current ##I## is sent through this wire. We know that if an electron is sent on a path which is perpendicular to the wire, towards it, with an initial speed ##v_0##, and the...
18. B Stupid question relating to electric induction

Hi, I've been interested in the science behind electrons/magnetism for quite a while. I've been learning quite a bit from various sources online. However there is one thing that's really nagging me. Magnetic fields result from moving electrons. That indicates that a permanent magnet has...
19. I Maxwell's Law of Induction - How Does it Work?

So, I was studying Maxwell's equations and I don't really understand the last one - Ampere's Law (with Maxwell's extra term added in). The bit I'm not able to understand is the term Maxwell added. How exactly does a changing electric field through a closed loop induce a magnetic field along that...
20. Induced EMF — generator coil area calculation

Homework Statement What is the necessary area for a generator that produces an emf of ##\mathcal{E} = 150V## when it spins at a ratio of 60 revolutions per second, in a magnetic field of ##B = 0.5 T##? Homework Equations ##\oint_{c} E \cdot dl = \mathcal{E} = -\frac{d}{dt}\iint_{s} B \cdot dS...
21. Proof via mathematical induction

Homework Statement Use mathematical induction to prove that (8n − 7n − 1) is divisible by 49 for any n ∈ N. Correction by mentor for better readability: ##49\,|\,(8^n-7n-1)## The Attempt at a Solution We can see that the base case is satisfied here: n = 1, 8^1-7*1-1 = 0 and 49 | 0 is true...
22. Winding Direction Consideration (Proper Winding)

Hello, I'm boy who suddenly been strucked by curiosity on how hand crank generator works and i watch and read some of how to create one, specially this one on youtube: and i want to create one but i don't have a 3D printer, but i saw some alternative but as i do/design my own coil based on...
23. Calculation of Change in Magnetic Flux Linkage Across a Wire

Homework Statement A straight wire of length 0.20m moves at a steady speed of 3.0m/s at right angles to a magnetic filed of flux density 0.10T. Use Faraday's law to determine the e.m.f. induced across the ends of a wire. Homework Equations E= Nd Φ/dt but N=1 so E= dΦ/dt The Attempt at a...
24. Solar PV:What happens to the lost energy?inductive recovery?

Hi there, I am new in here, thanks for any reply. I took same title of a previous closed 3D by pranj5. As understood main part of the energy absorbed by PV panels goes in reflection and heat. The heat origins mainly in electrons that are excited but not enough to jump or they jump but they...
25. I Faraday's Unipolar Induction Equation

Hello all, I have a question regarding Maxwell's Equations and Faraday's unipolar induction equation. If we study the case of a cylindrical magnet with a radius of r which is rotating about its axis with angular velocity w. The electrons within the magnet collide with the moving atoms, causing...
26. Calculate the induced EMF for angle α

I have a question in my book and it’s confusing me a bit. I tried to search online for similar solved problems but couldn’t succeed. So here it goes: Calculate the induced EMF in a conductor loop when the angle between \vec{A} ~ and~ \vec{B} ~is~ changed ~from ~{0 °}~ to ~{α °} in 1...
27. Induction: Electromagnet and Aluminium Ring

I need some help with this task, I am stuck. 1. Homework Statement An aluminium ring is placed on top of an elctromagnet. a. The electro magnet is connected to AC. What will happen with the aluminium ring? Motivate your answer. b. What will happen with the ring if the electromagnet is...
28. Sign of the Faraday-Lenz equation

Homework Statement Hello, good afternoon, I have a question that's coming up when I'm doing electromagnetic induction exercises. In some exercises they ask me to determine the electromotive force (iee), and when they do the exercise resolution they do it with absolute value. In other...
29. I Hilbert's omega rule, induction, omega-consistency

As I understand Hilbert's omega rule for a first-order proposition P over the natural numbers, P(0) &P(1) &P(2) &..... ⇒ ∀n∈ℕ P(n) :star: which seems to be the same as ω-consistency. Is there a difference? Further, the axiom schema of induction has each axiom for a proposition P over the...
30. Optimal values for power in an induction heater?

I really want to build a simple but powerful induction heater for hobby blacksmithing. Metal shaping and the design of the cooling system within the coils are not a problem. I need help understanding the electronics Obviously I must first use a transformer as a safety against "backlash" to the...