# Tagged Questions

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### Flux through planes of a wind turbine [on hold]

The question asks how much wind will flow through each plane of a cube surrounding the turbine. the velocity of the wind is given by a function that depends on position according to v=(az,bz^2,c). The ...
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### DC Generator with magnet as rotor

DC generators convert the AC current in them by split ring commutators right and the graph of the current will be like this but the question is how would be the graph if the magnet is the rotor and ...
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### Maxwell equations in cylindrical coordinates [on hold]

Give a coil of radius $R$ and $N$ turns crossed by a mean current of $I_0$ ampere at $10 MHz$ frequency (sinusoidal), I need to calculate the behaviour of the electrical and magnetic field inside the ...
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### How to calculate the Induced Voltage Given Spinning Conducting Loop? Intro to Electromagnetics problem [closed]

I'm having trouble figuring out a different variation of this problem. On my homework, I'm asked to find the induce emf for the following B field: $$\vec{B}=50\vec{a_y}$$ I was able to figure out the ...
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### Stern-Gerlach experiment theory question [closed]

I have an assignment problem which I've been having some difficulty with. i know the answer but I want to know how to arrive at it correctly, and want to know where I've gone wrong. Determine the ...
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### Estimating the rotational speed of DC motor

What is the best strategy to roughly estimate the RPM of a simple DC motor as seen in this video?. I want to estimate the max possible rotation of the coil that has $n$ number of turns and has moment ...
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### Net Electrostatic Field inside a Conductor is $\vec{0}$

I've heard an explanation for this, and my professor wasn't really able to clarify my questions, so I was hoping someone could help: Suppose there is an electrostatic field $\vec{E_{net}}\ne\vec{0}$, ...
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### Non-stationary capacitor

A common exercise in non-stationary electromagnetism is to find the electric and the magnetic field generated by a capacitor with round plates, if the potential difference between the plates varies in ...
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### Finding the magnetic vector potential by calculus of variations

Given the functional $$F[A]=\int_{\mathbb{R}^3}\{\frac{1}{2\mu(x)}|\nabla\times\vec{A}|^2-\vec{J}\cdot\vec{A}\}d^3x$$ with $\vec{A}$ is a candidate vector potential for the field ...
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### Current in an RC circuit inside in a magnetic field

Does my question make any sense? Context: The capacitor is charged with charge $Q_0$. There is a magnetic field $B=B_0 \hat{z}$ perpendicular to the monitor's screen. The length of the (AB) wire is ...
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### Can we explicitly solve the Hamiltonâ€“Jacobi equation for a particle in a uniform magnetic field?

HJE for nonrelativistic charged particle in an electromagnetic field is $$\frac{1}{2m}\left(\nabla S - q\mathbf{A}\right)^2 + q\phi + \frac{\partial S}{\partial t} = 0.$$ For a uniform magnetic ...
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### Prove Biot-Savart law, assuming that $\vec{A}=\frac I c\int \frac{d\vec{L}}{r}$

Prove Biot-Savart law, assuming that $$\vec{A}=\frac I c\int \frac{d\vec{L}}{r}$$ $$\vec{B}=\nabla\times \vec{A}$$ Any hint on what to do next?
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### How to compute speed without knowing mass or charge values?

A gold nucleus is 460 fm (1 fm = 10^(-15) m) from a proton, which initially is at rest. When the proton is released, it speeds away because of the repulsion that it experiences due to the charge on ...
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### Alignment of a system in equilibrium and its potential energy

Consider a flexible free conductor which is placed near a strong long bar magnet. How will the the conductor arrange itself if current is passed through it? I asked my professor: he gave me a hint ...
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### Torque due to a magnetic field

We have two infinite perpendicular wires, each carrying a current "i" and the distance between them is l. If both the wires are free to move, how will they arrange themselves because of the torque ...
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### Looking for a simple proof of symmetry of linear susceptibility tensor

Getting a diagonal susceptibility tensor: Define the linear susceptibility tensor as $\chi_{ij}$: $P_i = \epsilon_0\chi_{ij}E_j$, using standard notation for the electric field and the polarization. ...
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### Coefficient matrix of quadratic Lagrangian

I've been studying path integrals from Weinbergs QToF vol 1. He says that when the $\mathcal{L_0}$ is quadratic in fields we can always write free term $I_0$ in the generalized quadratic form ...
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### Very short physics question (electromagnetic field): Just draw the figure of the problem? [closed]

Can you please draw me the figure of the problem? I dont want the solution,just the figure? A straight, stiff, horizontal wire of length 25 cm and mass 50 g is connected to a source of emf by light, ...
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### Ampere's law and external currents

In Ampere's law the current outside the curve taken is not included in the expression. Does this mean that only the currents crossing the area bounded by the curve taken contribute to the magnetic ...
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### An electromagnetic induction problem [closed]

The question goes like this : A thin non conducting horizontal disc of mass $m$ having total charge $q$ distributed uniformly over its surface, can rotate freely about its own axis. Initially ...
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### Calculating the magnetic field due to a rotating ring using Biotâ€“Savart law

I wish to calculate the magnetic field due to a charged ring rotating about an axis perpendicular to the plane of the ring and passing through a point on its circumference $(P)$. I arrive at something ...
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### Proving the equivalency of the potential energy of a system of charges and the work required to assemble a system of charges

This is a very cool, and highly beneficial problem in my opinion. I feel as though truly understanding this proof would broaden anyone's conceptual understanding of electric potential. My textbook ...
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### Flaw in the radius of a spherical electron model (classical electron radius)

My textbook asks me to derive an equation for the potential energy ($U$) of sphere ($r_0$) filled with an electric charge of uniform density ($\rho$), expressed in terms of the total charge $Q$. The ...
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### In which loop does the induced emf remain constant during the passage out of the magnetic field region?

A rectangular loop and a circular loop are moving out of a uniform magnetic field to a field-free region with a constant velocity V as shown in the figure. Explain in which loop do you expect the ...
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### What would Maxwell's Equations be if we had magnetic charges and magnetic currents?

Mind you, we still have electric charge and electric currents. But, what would Maxwell's equations look like if we had to take magnetic charges and magnetic currents into consideration? Would there be ...
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### Post Problem Analysis - Rod in a cylindrical time varying magnetic field?

A metal rod of length $l$ is placed (as shown in figure) in a cylindrical time varying magnetic field. Find the potential difference across it. My answer: As electric fields as forming circles ...
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### Electromagnetic waves and boundaries

I am reading about dielectric boundaries and electromagnetic plane waves following griffiths ch7. When considering a boundary at z=0 with electric fields perpendicular to the plane of incidence it ...
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### Magnetic field above center of current-carrying loop

A current $I = 2A$ flows in a circular loop coil of radius $R = 10 cm$. Evaluate the magnitude of the magnetic field (in Tesla) at a point $P$ on the axis of the coil, and a distance $z=5cm$ away ...
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### Maxwell calculations that predicted the generation of waves (further use for wireless telegraphs)

At this point in this documentary about the history of electricity: https://www.youtube.com/watch?v=oPnS2WO2_0k&t=4m40s the guy says the Maxwell calculations predicted the generation of certain ...
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### Determine stationary angular velocity of wheel with circuit in magnetic field

I have a wheel (free to spin around the $z-$axis) with four spokes that is connected by sliding contacts to a circuit with $U_0 = 0,72V$. Also, there is a B-Field parallel to the $z-$axis For the ...
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### Why a transistor is activated when I touch its base with my finger? [closed]

Is my body charged eletrically? If so, how much? Will it work with all types of transistors?
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### A question on an exercise from Gravitation by Misner, Thorne and Wheeler

My question is on problem 4.1 of Gravitation. In a generic case of electric field and magnetic field(i.e not $E=0$ or $B=0$ or $E$ and $B$ perpendicular), define the direction $\hat{n}$ unit vector , ...
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### Uniformity in a solenoid

I know the magnetic field strength increases as the number of turns in the solenoid increases. However, I've learnt the field inside the solenoid is usually nearly uniform. So, does the number of ...
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### Why is the inner product between divergence-free current$\vec{J}$, (satisfied $\nabla\cdot\vec{J}=0$) and a gradient field$\nabla \varphi$ zero?

I read a statement saying that the inner product between divergence-free current and a gradient field is zero. Divergence-free surface current is $\nabla\cdot\vec{J}=0$, and $\vec{J}$ could be ...
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### Direction of current flow

In one of my homework questions, I was given the following setup. I was asked to determine if the induced current flows from X to Y, or from Y to X. From Lenz's Law I know that the current in the ...
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### Torque per unit length on infinite rotating charged cylinder

For homework I have the following question, but I am stuck on finding the torque on the cylinder. An infinite cylinder of radius $R$ carries a uniform surface charge $\sigma$. We start rotating the ...
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### Electric Potential of a sphere given electric field

I'm studying for a course in electromagnetism, and I've been given an electric field for which I need to find the associated scalar potential. The field is the field generated by a sphere of radius ...
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### Potential in the middle of a square [closed]

Find the electric potential in the middle of a square with side length $a$ and charge $Q$. If I put the origin in the middle of the square, for the potential I get: ...
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### Solving electromagnetic vector field using the Lagrangian

Given an action of the form $$S=-\frac{1}{4}\int d^4x\eta^{\mu\nu}\eta^{\lambda\rho}F_{\mu\lambda}F_{\nu\rho}$$ where ...
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### Is the dielectric constant of an insulator always positive?

I know there are many examples of metals with a negative dielectric constant at optical frequencies. But what about insulators?
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### Sphere in homogenou magnetic field

I have to find out the magnetic dipole moment of sphere in homogenou magnetic field in the limit $\mu_r\rightarrow+\infty$. I don't know what does the condition $\mu_r\rightarrow+\infty$ mean. Does ...
Two small wire loops, each with radius b, are placed a distance $d >> b$ apart. The loops are oriented as shown below; i.e., both loops lie in the x-y plane. Each loop carries the same current ...