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# rotating cylinder in uniform magnetic field

## Dielectric Cylinder That Rotates in a Uniform Magnetic Field

2015-5-23  cylinder of relative dielectric constant εr rotates with constant angular velocityωaboutits axis. A uniform magnetic ﬁeldBis parallel to the axis, in the same sense as ω. Findthe resulting dielectric polarizationPin the cylinder and the surface and volume chargedensitiesσandρ, neglecting terms of order (ωa/c)2,whereais the radius of the cylinder.This problem can be conveniently analyzed by starting in the rotating

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## TRANSIENT SIMULATION OF A ROTATING CONDUCTING

2017-3-28  To study this, transient finite element analyses were conducted to simulate the magnetic field inside a rotating solid conducting cylinder immersed in a uniform transverse magnetic field, such as earth’s magnetic field.

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## Magnetic field inside of a long rotating cylinder

2015-12-21  The cylinder rotates around its axis with angular speed $\omega$. All of the parameters are constants. I've tried using Amper's law but I can't seem to get to the right answer. $J=\lambda \cdot v=\sigma\omega R dr$ $I=\sigma \omega R L$ L is just the the part of the length of the whole cylinder. So I i'll just use Amper's law :

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## Electromagnetic Angular Momentum of a Rotating

2020-7-27  In contrast, magnetic ﬁeld lines always form close loop, as magnetic charges do not exist(as far as we know). Hence, it is less clear that the magnetic ﬁeld lines rotate along with thecharged cylinder. Indeed, Faraday’s view (secs. 218 and 220 of, and sec. 3090 of)was that the magnetic ﬁeld lines do not rotate in this case.2

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## Understanding Ferrofluid Spin-Up Flows in Rotating

infinitely long cylinder. A uniform externally applied field to a sphere results in a uniform internal magnetic field since a sphere has Nx=Ny=Nz=1/3. Only in an infinitely long cylinder with transverse magnetization with Nx=Ny=1/2 and Nz=0, is the field uniform. A finite height cylinder will have spatially non-uniform demagnetizing factors

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## Electromagnetic Angular Momentum of a Rotating

2020-9-16  The rotating cylindrical shell of charge produces a solenoidal magnetic ﬁeld, which is given in the approximation of an inﬁnite cylinder as, B = ⎧ ⎨ ⎩ 2λω c ˆz (ra). (2) 1

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## Magnetic field of rotating cylinder Physics Forums

2007-12-12  I made a picture of the problem to illustrate this. The only hint given: "the magnetic field outside the cylinder is zero. Homework Equations Sorry, I cannot use Latex, but: integral(B,ds) = u0*integral(J,da) where B is the magnetic field, ds the vector line element, J the current density, da the vector area element. The Attempt at a Solution

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## Eddy current in a rotating cylinder in a static field by a ...

2021-7-9  Fig. 1. Rotating cylinder in a constant magnetic field The whole considered domain, air and rotating cylinder regions, is a square. On two sides of the domain, we have Neumann’s condition and on the other sides, the value of the magnetic vector potential is imposed, either a constant or its opposite.

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## Perfectly Conducting Cylinder in an External, Static ...

2019-7-27  Then, if the cylinder is not rotating, there are no charge or current distributions associated with the cylinder, and the electric ﬁeld remains zero. If the cylinder rotates with angular velocity ω about its (z) axis, an axial eddy-current density J z(r,φ) is induced (plus radial currents at the ends of the long/inﬁnite cylinder) by

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## Magnetic field in a rotating uniformly-charged infinite ...

2020-5-28  3,884. 1,524. The only argument I see now is based on symmetry. Due to cylindrical symmetry we can argue that the field outside the cylinder will be in the z-direction. But again due to symmetry we cant decide if it will point in the up or down direction. So

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## Linear stability analysis for a rotating cylinder with a ...

2004-5-18  This paper treats the first hydrodynamic instability for a uniform-density, electrically conducting liquid in a finite-length cylinder which is rotating about its centerline. There is a uniform, transverse magnetic field which rotates about the cylinder’s centerline and which produces a steady, axisymmetric, azimuthal body force on the liquid. For the initial transition from a steady ...

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## TRANSIENT SIMULATION OF A ROTATING CONDUCTING

2017-3-28  simulate the magnetic field inside a rotating solid conducting cylinder immersed in a uniform transverse magnetic field, such as earth’s magnetic field. The factors that affect the magnetic field inside the cylinder were analyzed by varying the spin rate and the electromagnetic physical properties (conductivity and permeability) of the cylinder.

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## Understanding Ferrofluid Spin-Up Flows in Rotating

COMSOL models of an infinitely long ferrofluid filled cylinder, with zero spin-viscosity, subjected to a non-uniform field imposed by an infinitely long permanent magnet in addition to a uniform rotating magnetic field results in significant flow. These flows are also observed experimentally when subjecting a ferrofluid filled sphere to a non ...

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## Magnetic field of rotating cylinder Physics Forums

2007-12-12  Homework Statement. The problem is to find the magnetic field within a rotating cylinder (infinitely long) that has on its surface a given surface charge density p. I made a picture of the problem to illustrate this. The only hint given: "the magnetic field outside the cylinder is zero.

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## An Analysis of Spin Diffusion Dominated Ferrofluid Spin

2011-12-1  Keywords: ferrofluids, uniform rotating magnetic fields, spin-up flows, spin diffusion, ferrohydrodynamics 1. Introduction The classic spin-up experiment involves placing a ferrofluid filled cylinder in a uniform rotating magnetic field and observing the velocity distribution. The opacity of

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## electromagnetism - Magnetic field inside a rotating ...

2018-6-14  However, a good estimate of the magnetic field, even when there is some displacement current present, is usually possible to obtain by using the Biot-Savart law. For cylinder with surface current, it turns out that the magnetic field inside calculated that way is uniform

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## Magnetic field in a rotating uniformly-charged infinite ...

2020-5-28  3,884. 1,524. The only argument I see now is based on symmetry. Due to cylindrical symmetry we can argue that the field outside the cylinder will be in the z-direction. But again due to symmetry we cant decide if it will point in the up or down direction. So

More

## Eddy current in a rotating cylinder in a static field by a ...

2021-7-9  Fig. 1. Rotating cylinder in a constant magnetic field The whole considered domain, air and rotating cylinder regions, is a square. On two sides of the domain, we have Neumann’s condition and on the other sides, the value of the magnetic vector potential is imposed, either a constant or its opposite.

More

## Electromagnetic Fields of a Rotating Shell of Charge

2015-5-23  Thus, inside the shell the magnetic ﬁeld is uniform, and outside the shell it has the form of a point dipole whose strength is the total magnetic dipole moment of the rotating shell, 2 B(ra)= 3(m ˆr)ˆr− m r3. (14) 2.2 Electrodynamics in a Rotating Frame 2.2.1 Summary of the Principles

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## Location of stagnation points for a rotating cylinder in

The Location of stagnation points for a rotating cylinder in a uniform flow field formula is known while considering the sin inverse with a ratio of circulation to the freestream velocity and the radius of the cylinder and is represented as θ = - asin (Γ /(4* pi * V ∞ * R)) or angle_at_stagnation_point = - asin (Circulation /(4* pi * Freestream Velocity * Cylinder Radius)).

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## Linear stability analysis for a rotating cylinder with a ...

2004-5-18  This paper treats the first hydrodynamic instability for a uniform-density, electrically conducting liquid in a finite-length cylinder which is rotating about its centerline. There is a uniform, transverse magnetic field which rotates about the cylinder’s centerline and which produces a steady, axisymmetric, azimuthal body force on the liquid. For the initial transition from a steady ...

More

## Understanding Ferrofluid Spin-Up Flows in Rotating

COMSOL models of an infinitely long ferrofluid filled cylinder, with zero spin-viscosity, subjected to a non-uniform field imposed by an infinitely long permanent magnet in addition to a uniform rotating magnetic field results in significant flow. These flows are also observed experimentally when subjecting a ferrofluid filled sphere to a non ...

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## INSTABILITY OF ROTATING MAGNETIC FIELD ...

2005-6-15  1. Experimental procedure. Let a regular cylinder of a diameter equal to its height ﬁlled with mercury rotates with a constant angular frequency −Ωin a uniform rotating magnetic ﬁeld with an amplitude B0 and an angular frequency ω0. The task consists in ﬁnding conditions under which the stationary ﬂow inside the cylinder will be stable.

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## Magnetic field in a rotating uniformly-charged infinite ...

2020-5-28  3,884. 1,524. The only argument I see now is based on symmetry. Due to cylindrical symmetry we can argue that the field outside the cylinder will be in the z-direction. But again due to symmetry we cant decide if it will point in the up or down direction. So

More

## Rotating magnetic field effect on convection and its ...

2021-6-21  Rotating magnetic field effect on convection and its ... of the cylinder (1 .5 6 A 6 10) is shown to strongly aﬀect ... and eventually decreases more slowly until A = 10. The RMF used in most crystal-growth processes is a spatially uniform, transverse magnetic ﬁeld which rotates at a constant angular velocity, ω, around the centreline ...

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## On the motion of a rigid cylinder in a rotating ...

The flow structures generated and drag experienced by a rigid cylinder moving in an arbitrary direction through a rotating electrically conducting fluid in the presence of an applied magnetic field are investigated, with the aim of understanding better the nature

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## Liquid metal flow in a finite-length cylinder with a ...

A liquid metal flow induced by a rotating magnetic field in a cylindrical container of finite height was investigated experimentally. It was demonstrated that the flow in a rotating magnetic field is similar to geophysical flows: the fluid rotates uniformly with depth and the Ekman layer exists at the container bottom. Near the vertical wall the flow is depicted in the form of a confined jet ...

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## Ferrofluid surface and volume flows in uniform

Ferrofluid surface and volume effects in uniform dc and rotating magnetic fields are studied. Theory and corroborating measurements are presented for meniscus shapes and resulting surface driven flows, spin-up flows, and Hele-Shaw cell flows and instabilities. To characterize the water-based and oil-based ferrofluids used in experiments ...

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## Electromagnetic Fields of a Rotating Shell of Charge

2015-5-23  Thus, inside the shell the magnetic ﬁeld is uniform, and outside the shell it has the form of a point dipole whose strength is the total magnetic dipole moment of the rotating shell, 2 B(ra)= 3(m ˆr)ˆr− m r3. (14) 2.2 Electrodynamics in a Rotating Frame 2.2.1 Summary of the Principles

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## The simple loop is rotating in a uniform magnetic field ...

The simple loop is rotating in a uniform magnetic field shown in Figure has the following characteristics: B =1.0 T to the right r =01. m l =0.3 m { \omega }_{ m } = 377 rad/s (a) Calculate the voltage { e }_{ tot } (t) induced in this rotating loop. (b) What is the

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