What is Toroid: Definition and 67 Discussions

In mathematics, a toroid is a surface of revolution with a hole in the middle, like a doughnut, forming a solid body. The axis of revolution passes through the hole and so does not intersect the surface. For example, when a rectangle is rotated around an axis parallel to one of its edges, then a hollow rectangle-section ring is produced. If the revolved figure is a circle, then the object is called a torus.
The term toroid is also used to describe a toroidal polyhedron. In this context a toroid need not be circular and may have any number of holes. A g-holed toroid can be seen as approximating the surface of a torus having a topological genus, g, of 1 or greater. The Euler characteristic χ of a g holed toroid is 2(1-g).

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  1. C

    Calculating Electric Potential for a Non-Negligible Thickness Toroid

    For A.1 of this problem, The solution is However, I have a doubt about the linear charge density ##\lambda##. I don't understand how ##\lambda = \frac {q}{2\pi R} ## since this is not a thin ring, but has a non-negligible width of ##2a## I think that the toroid has a larger area than thin...
  2. V

    Engineering What is the magnetic field of a half toroid?

    Hello, I would like to know what is the magnetic field of a half toroid. Would we use Ampere's law? So, considering that the integral is equal to BA, we would have BA = μo * i, then B = (μo * i) / r. But, using Biot-Savart's law, by symmetry, it seems that the vector sum of all the...
  3. Shreya

    Understanding the Plasma Confinement in Tokamak Reactor

    Please be kind to help. How is an electric field formed due to toroidal magnetic field? How does the introduction of a poloidal magnetic field confine the plasma? Please answer in the context of Nuclear Fusion Reactor (tokamak).
  4. D

    Inductance of Parallel Coils on an uncut toroid magnetic core

    Hi, I have a toroid of a soft magnetic material (any). I wind the complete toroid with single turn coils and connect all their terminals in parallel. Then I wind a second layer of single turn coils on the previous layer and so on. I want to calculate the equivalent inductance L. I calculate it...
  5. P

    Ampere's Law for a toroid (finding relative permeability of iron)

    Why is this equation: B(D - d)/mu + Bd = mu0 N I true? B = magnetic field in the hole of the toroid D = Average diameter of the toroid d = Diameter of hole of toroid mu = relative permeability of iron, or whatever the toroid is made of mu0 = 4pi x 10^-7 N = Number of turns on the toroid I =...
  6. H

    Finding Magnetic Field of a Toroid with Two Circuits

    I have a toroid with square cross section and 2 different circuit: ##C_1## where ##N=N_1## and ##I=I_1## ##C_2## where ##N=N_2## and ##I=I_2## I have a question that say I have to find the magnetic field ##B## produce by ##C_1## everywhere inside the coil. I assume here I have to find the...
  7. A

    Magnetic mirror: pentagon or hexagon toroid?

    I know that the problem of magnetic mirrors is that they leak out the tight ends of the mirror, on the other hand the main problem of toroids is that magnetic field line curvature creates a better confinement on the inner diameter and lesser on the outer diameter so needs a strong plasma current...
  8. Adesh

    Why does the current have no ##\phi## component in a toroidal coil?

    These are images from the book Introduction to Electrodynamics by David J. Griffiths . . . My problem is that I'm unable to understand how the current has zero ##\phi## component (I have underlined it in the first image)? I do understand cylindrical coordinates, I know...
  9. A

    What materials are used for the tokamak toroid wall?

    There are two questions that arose in my mind, first of all tokamaks use toroidal field coils which create a toroidal field within the torus to shape the plasma and confine it, but here is a question, the toroid coils have a static B field produced from a DC current in them, what kind of metal...
  10. J

    Winding a toroid inductor, is this calculation correct?

    Hi, I am going to wind an tapped toroid inductor for a LCR circuit in an equalizer. I have calculated the number of turns I need for each winding. This is my first time winding an inductor so I need to get some things straight. What to do with the 10 kHz tap, should I twist a wire with the 12...
  11. T

    Toroid with Air Gap magnetostatics problem

    Homework Statement consider a toroidal electromagnet with an iron ring threaded through the turns of wire. The ring is not complete and has a narrow parallel-sided air gap of thickness d. The iron has a constant magnetization of magnitude M in the azimuthal direction. Use Ampere's law in terms...
  12. R

    Self-inductance of a toroid with a rectangular cross section

    I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?
  13. S

    Vector Potential of a Toroid

    I am sure that the vector potential of a toroid isn't 0 even though its magnetic field is , does anyone have a derivation for the its the vector potential at a point P(x,y,z) outside the toroid ? i expect that since its curl is 0 we have a general form of : A = f(!x)ex + g(!y)ey+m(!z)ez Such...
  14. Ryan Doucette

    Nuclear Fusion: Electron Thermal Transport Terminology

    I am an undergrad physics major in my final semester currently taking Intro to Thermodynamics. As a final project, each student must choose a topic related to thermodynamics that is more advanced than what is covered in the curriculum and write a paper and present our findings to the class on...
  15. Pushoam

    Direction of magnetic field due to a toroid

    Homework Statement To find the direction of magnetic field due to a toroid. Homework EquationsThe Attempt at a Solution Taking the cross - sectional shape of toroid circular, the toroid could be turned into a solenoid. A solenoid's magnetic field is along its axis. When the solenoid gets...
  16. G

    I Induced EMF in a half vs. whole ferrite toroid

    Hello all - I've stumbled upon what seems to be a pretty basic magnetic materials question that's got me stumped. Maybe one of you can help me figure this out. I did the following experiment (see figure below): Put a ferrite toroid around a current carrying wire carrying 12 Amps RMS at 120V...
  17. A

    Magnetic flux in Toroid?

    Homework Statement The general method to find the total magnetic flux through an object is found by: Φ =∫B*ds (dot product) what is the ds over which we take the integral on?? what surface is it?, is it the surface over which the magnetic flux enters? Homework Equations Φ =∫B*ds (dot product)...
  18. M

    I Movement of a iron ring inside a toroidal solenoid

    What happens when you apply power to a toroidal solenoid with a iron ring inside? Does the ring move? Does the speed of movement depend on the amount of power? Sorry if this is too easy, I have no education in physic.
  19. S

    Electromagnet magnetic field strength

    Homework Statement Homework Equations ##\oint_{C} Bd\ell = \mu I_{enc}, B_{normal}## continuous across boundary, ##H_{parallel}## continuous across boundary The Attempt at a Solution $$\oint_{C} Bd\ell = \mu I_{enc} \rightarrow B = \frac{\mu NI}{2\pi r}$$ Any help much appreciated. How...
  20. P

    Spinning Toroid shaped objects

    In our class we were playing with a toroid shaped object made of foam (Probably). While tossing it around, not only was the disc rotating simply. It was well, sort of vibrating. Like one end of the object is up and the other is down then after a small interval the vice versa occurs. What is the...
  21. S

    How does a partially wound toroidal core affect magnetic force and field flow?

    Hi all.. I am currently working on a project where i need to wound toroidal core halfway (not completely) so that part f the core is exposed. With that part, I need to lift weight a certain amount of weight (not fixed at this point). I am trying to understand what kind of equations would be...
  22. M

    Magnetic field of a Toroid

    Layman speaking here.. I have for a while been interested in a small desk toy. It is a magnetic levitating globe. There is a doughnut shaped electromagnet at the base which according to the internet is a toroid. Within the globe sits a disc shaped neodymium magnet. The globe hovers barely a...
  23. A

    Magnetic Field Inside a Toroid

    Homework Statement A toroid has a 49.4-cm inner diameter and a 57.4-cm outer diameter. It carries a 23 A current in its 500 coils. Determine the range of values for B inside the toroid. A) Bmaximum = ? B) Bminimum = ? Homework Equations B = mu0/2pi * NI/r[/B] The Attempt at a Solution I...
  24. A

    Help Needed: Building a Tesla Coil - No Arcs Coming Out Toroid

    Hello all, I am in the process of building a tesla coil and I need a little help. I have everything completed enough that I can start testing it. I plug the coil in and the spark gap fires immediately and continuously, but no arcs come out the toroid. I tried moving the toroid closer to the...
  25. D

    Find field intensity at center of toroid?

    Homework Statement I really think my answer is correct - could someone verify this or let me know where I went wrong? This is problem submitted online, the "correct" answer looks like my teacher accidentally hit the button 3 twice. PROBLEM: The toriod in example 5-1 from the textbook has an...
  26. T

    Total internal confinement of magnetic field

    Hi, I heard it was possible if you symmetrically wind a toroid that you can get near total internal confinement of the magnetic field in the axial plane inside the toroid. How is this possible? I imagine a section of a closed loop of wire on the face of the toroid core, yet I still imagine those...
  27. A

    Calculating the B field in a small gap in a toroid

    Homework Statement Take a steel core (K_m = 2500) electromagnet, bend it into a loop with a small air gap, and determine the B field in the gap. The cross-sectional area of the toroid is 4cm^2, and the air gap is 2.5mm. The current through the coil's 120 turns is 15 amps. The radius of the...
  28. K

    Helical Toroid Equation

    Homework Statement The equation below describes a helical toroid I need a way to define pitch and chirality, if someone can please help me with these functions. I found this equation on the internet, but it's greek to me Homework Equations <cos(t)(R1+R2 cos(βt)),sin(t)(R1+R2...
  29. E

    Calculating Radial Distance in a Toroidal Coil: Step-by-Step Guide

    Radial Distance In class, I measured the field strength of a toroidal coil at various distances. I used a linear track to move the hall probe along the azimuthal field at certain positions. How do i convert the distance into radial distance if the inner conductor is at radius 2.5 cm?
  30. O

    Why is the magnetic field outside a toroid 0?

    Finding the magnetic field for a straight wire using the right hand rule shows that the field is around the wire. Applying this same concept for a toroid, the magnetic field inside is central to the loop of wires so that makes sense. However, isn't there also a magnetic field outside in a...
  31. ugenetic

    Maxwell's 4th equation for a Toroid

    Thank you for reading this. the circuit is simply a SinWave voltage source (ideal) connected to a single coil with an closed iron core inside. It would like the picture below while ignore the labels: Only consider saturation and hysteresis of the core and assuming no resistance,no...
  32. baby_1

    Electromagnetics density of Toroid

    Hello I have some problems to obtaining Electromagnetic density via Ampere's Law. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indtor.html my problem is why we don't calculate and sum Inflow and outflow of Ampere's closed loop path.to clearing my question please take a look at below...
  33. R

    Ampere's Law when applied to a toroid

    It's a simple question: Why is Ienc in Ampere's Law in a toroid equal to µ0NI where N is the number of loops around the toroid? Why is I N times greater when the wire is looped around the toroid? When you take a random wire with current and you change the geometry of the wire into a loop...
  34. S

    Magnetic Field of a Toroid

    Homework Statement "The toroid shown in the figure has a wire carrying a current I= 7.80 Amperes wrapped around it N= 920 times. The inner radius is R1 14.0 cm and outer radius R2 16.8cm. What is the magnitude of the magnetic field along a circle that is halfway between the inner and outer...
  35. R

    Magnetic Field of A Toroid

    Homework Statement I'm working through a proof that says the magnetic field of a toroid is circumferential at all points inside and outside the toroid. I can follow most of the proof, but am a bit confused where the first equation comes from. Here is the figure from the textbook (Griffith's...
  36. L

    Lorentz force in a toroid coil

    Hi, I'm having a major issue trying to work out where the resultant lorentz force might act when I have a wire coiled around a doughnut (toroid) shape. Am I right in saying that there will be a resultant lorentz force acting to crush the doughnut because there will be a slightly denser...
  37. Saitama

    Magnetic field at centre and inside the toroid

    Homework Statement ##N=2.5\times 10^3## wire turns are uniformly wound on a wooden toroidal core of a very small cross-section. A current ##I## flows through the wire. Find the ratio ##\eta## of the magnetic induction inside the core to that at the centre of the toroid. Homework Equations...
  38. B

    RLC circuit driven by a 'Real' toroid

    I'm currently wanting to model an RLC circuit that is driven by a toroid transformer with a driving current, I(t). See image below. In physics class, I've done similar problems with 'ideal' toroids and a simple R circuit. What I'm struggling with is how to model a 'real' toroid...
  39. F

    Calculating Capacitance of a Toroid: Formula and Proof

    Hi, I am new here. I need to know the formula for the capacitance of a toroid of circular cross section. I found this: http://deepfriedneon.com/tesla_f_calctoroid.html But I need to show the proof for the formula. Can anyone help?
  40. M

    What happens to a permanent magnet inside a electromagnetic toroid?

    Suppose a permanent bar-magnet is placed inside a toroid/torus and the toroid is then completed and power applied. How will the magnet move? Will it move?
  41. R

    Toroid and Solenoid Flux

    This is more a theoretical question than a practical one. Basically I want to know if the formulas I arrive for the flux of a Toroid and a Solenoid are correct Leaving aside the integration part this is the basic formula for the flux \phi = BNA B = magnetic field N = number of turns of...
  42. R

    Ferrite magnet as toroid transformer

    Dear Experts I have a 1.5 cm ring magnet, you know, the black color type of common low magnetic power magnet. I wrapped 5 turns of copper wire around it on one side and then wrapped 10 rounds of another copper wire around it . I connected 5v battery to the 2 ends of the primary coil which...
  43. C

    Magnetic Field in a rectangular toroid

    Consider a toroidal structure with a rectangular cross-section. If the toroid is defined by the surfaces r = 1cm and r = 4cm and the planes z = 0 cm and z = 2 cm, and the surface current density on the surface defined by r = 4cm is given by -60az A/m. (a) Specify the current densities on...
  44. Ray Fischer

    From the two geometries of a Toroid and a Mobius ring: Torbus

    I have made a geometry, see first attachment, I call the “Torbus”, from the two geometries of a Toroid and a Mobius ring, though the twisted ring cut from a torus is not the classical Mobius ring. I have not been able to derive the math (too many variables) that describes the movement of the...
  45. W

    Mutual inductance of a solenoid wrapped around part of a toroid

    *This isn't a problem so much as needing to fill in the gaps from a lecture where I was taking notes on painkillers due to surgery. The problem statement is my best guess as to what exactly was said by the instructor. Homework Statement "Find the mutual inductance (M) of a square-bore...
  46. R

    Toroid of Circular Cross-section

    Homework Statement A toroid of circular cross-section of radius a and mean radius r_{m}. Show that the inductance of this coil is given by L = μ_{r}μ_{o}N^{2}[r_{m}-(r_{m}^2-a^{2})^{1/2}]. Homework Equations The B-field of a toroid: B = μNI/2πr (phi-direction)The Attempt at a Solution Total...
  47. P

    Solenoid and toroid inductance puzzle

    Im working with building a reluctance motor and I've posed a problem to myself that i cannot answer without questioning some long accepted facts about the inductance of a solenoid. The simple solenoid and toroidal solenoid are two shapes that seem to have simple equations for calculating the...
  48. C

    Is the B Field Constant Inside a Toroid?

    Is the B field constant inside a toroid? Like we would just use amperes law to find. B(2*pi*r)=(mu_0)NI But after talking to this kid he said it changes inside. But i thought it was constant.
  49. D

    Magnetic field of a toroid

    The toroid shown in the figure has a wire carrying a current I= 7.10 Amperes wrapped around it N= 820 times. The inner radius is R1 23.0 cm and outer radius R2 27.6cm. Figure: http://capaserv.physics.mun.ca/msuph...ob01_torus.gif What is the magnitude of the magnetic field along a...
  50. D

    Magnetic field of toroid

    The toroid shown in the figure has a wire carrying a current I= 7.10 Amperes wrapped around it N= 820 times. The inner radius is R1 23.0 cm and outer radius R2 27.6cm. Figure: http://capaserv.physics.mun.ca/msuphysicslib/Graphics/Gtype63/prob01_torus.gif What is the magnitude of the...