What is B field: Definition and 173 Discussions

A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as a field of pseudovectors.
In electromagnetics, the term "magnetic field" is used for two distinct but closely related vector fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter (A/m). B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, the two fields are related through the vacuum permeability,




B


/


μ

0


=

H



{\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} }
; but in a magnetized material, the terms differ by the material's magnetization at each point.
Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force, one of the four fundamental forces of nature.
Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

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  1. fluidistic

    Charged particle in a B field, tensor notation

    Homework Statement A charged particle of charge q with arbitrary velocity ##\vec v_0## enters a region with a constant ##\vec B_0## field. 1)Write down the covariant equations of motion for the particle, without considering the radiation of the particle. 2)Find ##x^\mu (\tau)## 3)Find the...
  2. Robsta

    Square wire loop moving in a static B field.

    Homework Statement [/B] 3. A square loop of area a 2 is formed from a single turn of thin wire of resistance R. The loop is aligned with two sides parallel to an infinite straight thin cable, with its closest side a distance r away, and is given a velocity v in a direction perpendicular to the...
  3. Robsta

    Construct B field from a given E field using Maxwell's Eqns

    Homework Statement Given an electric field in a vacuum: E(t,r) = (E0/c) (0 , 0 , y/t2) use Maxwell's equations to determine B(t,r) which satisfies the boundary condition B -> 0 as t -> ∞ Homework Equations The problem is in a vacuum so in the conventional notation J = 0 and ρ = 0 (current...
  4. J

    Electron trajectory in B field with random energy kick

    So I wanted to get some second opinions on this situation I have thinking about.Lets say an electron enters, normally, a section of bfield that is perpendicular to its motion such that the electron will undergo circular motion. This is the simple part and is labeled as "E0" in the picture...
  5. applestrudle

    Proving the B field in a wire only has theta component?

    Homework Statement Prove in a current carrying wire the magnetic field only has a theta component. Homework Equations ∇ ⋅ B = 0 (dive of magnetic field zero, 2nd Maxwell Eq) ∇ x B = μ J (Ampere's Law, 4th Maxwell Eq) Cylindrical symmetry means B field only dependent on r (distance from z...
  6. Coffee_

    Force on a shrinking circular loop in a constant B field

    1. A conducting loop is shrinking in a constant ##\vec{B}##-field that is perpendicular to the loop-axis. The radius of the loop is given by ##r(t)=r_{0}e^{-at}##. The resistance in the loop is ##R(t)=2 \pi \rho r(t)##. What force is needed to keep the loop shrinking like this?2. Faraday's law...
  7. 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...
  8. fluidistic

    1-D Ising's model without B field, stat. mech., correlation

    Homework Statement Hi guys, I'm going nuts on a problem. Out of memory the problem was a system of N pairs of atoms that interact between each others so that the Hamiltonian of the whole systeme is ##H=-J \sum _{n=1}^N \sigma _i \tau _i## where the only possible values of the ##\tau _i##'s and...
  9. S

    Help with B field for a homemade electromagnet

    Homework Statement I'm doing a physics demo, and I've made basic electromagnet using some copper wire, a 6 volt battery, and a carbon steel screw, and I need help checking my calculations because I think the magnetic field for my magnet is too large. I've double checked everything and can't...
  10. A

    B field of cylinder with time-varying current

    Homework Statement In the picture in the figure, three coils are tightly wrapped around a non-magnetic cylinder of diameter Dcyl. Each coil is defined through the diameter of each wire comprising the coil, dcoil1-dcoil3, the current going through each coil, I1-I3, and the number of turns in...
  11. B

    Rotating Bar in uniform B Field

    Homework Statement A 1.60 m long rod rotates about an axis through one end and perpendicular to the rod, with a rotational frequency of 6.91 radians per second. The plane of rotation of the rod is perpendicular to a uniform magnetic field of 0.30 T. Calculate the magnitude of the mf induced...
  12. E

    What is the value of the B field in Teslas, inside the Helmholz coils?

    Homework Statement For a current of 2.5 amps, what is the value of teh B field in Teslas, inside the Helmholz coils in the e/m apparatus? Homework Equations B = 7.7 x 10^4 x I , I is the current in amps. The Attempt at a Solution B = B = 7.7 x 10^4 x 2.5 amps = .001925 = 1.925 x 10^-3Did I...
  13. I

    B field at Center of Conducting Square

    Hi there I am just really confused as to how they arrived at the answer to this problem. I attached a picture of the entire question and the solution. Homework Statement Please see attached file. Homework Equations Biot Savart Law for Magnetism of a Wire where the length of wire is much...
  14. G

    B field inside conductor with assymetric cavity

    Homework Statement Infinite straight conductor, parallel with z axis, of radius R1 with a cylindrical cavity of radius R2. The axis of the cavity passes through the point <0,b,0>. A current I flows through the conductor. The current density is homogenous inside the cundoctor. Find the...
  15. G

    Conducting rod is free to move over a loop under influence of B field?

    Homework Statement The conducting rod ab shown in the figure (Figure 1) makes contact with metal rails ca and db. The apparatus is in a uniform magnetic field 0.800 T, perpendicular to the plane of the figure. If the resistance of the circuit abdc is 1.50 Ω (assumed to be constant), find...
  16. M

    Radial component of B field of solenoid

    Hi everyone. I'm having a relatively hard time in understanding Griffith's explanation of why the radial component of a magnetic field of a solenoid should be zero. He says, "If B(r) were positive, if we reversed the direction of the current, B(r) would be negative. But switching I is...
  17. C

    Axial B field from disc of charge

    Homework Statement An insulating disc of radius a has uniform surface charge density σ and is rotating at constant angular velocity w about a perpendicular axis through it's centre. a)What is the surface current density ##\vec{j}(\underline{r})## at a position ##\underline{r}## relative to...
  18. B

    Why is the induced M field proportional to H, instead of the B field?

    The M field is the density of induced or permanent magnetic dipole moments. It is analogous to the P field in electrostatics. In electrostatics, the induced P field in a dielectric is proportional to the applied electric field. This is intuitive to me. Why though, in magnetostatics, is the M...
  19. B

    B Field Inside of Sphere using Sep. Variables

    Done editing I hope. Homework Statement If Jf = 0 everywhere, then (as we showed in class), one can express H as the gradient of a scalar potential, W. W satisfies Poisson’s equation with ∇⋅M as the source. Use this fact to find the field inside a uniformly magnetized sphere. (Griffiths has...
  20. C

    What is the magnetic field of two parallel current loops?

    Homework Statement Helmholtz coils can be modeled as a pair of current loops oriented so that they are parallel to each other with a common axis in the x direction. The two loops have the same current I, and the same radius R, and their centres are at x = -d and x = +d, so the distance between...
  21. K

    If I wanted a constant B field using an element

    Or some naturally occurring material what would I use. I'd like the strongest constant uniform magnetic field possible. Is there some sheet of material I can use?
  22. D

    Calculate the B field inside and outside a wire

    Homework Statement A long, straight wire of radius a has current density J = J0e−β(α−ρ)uz where β is a constant and ρ < α. Determine B inside and outside the wire.Homework Equations J=I/((pi)a^2) B=(μIρ)/(2(pi)(a)^2) The Attempt at a Solution Here is what I did B=(μρ/2)J0e^(-β(alpha-ρ))
  23. A

    Direction of induced electric field due to uniform B field decreasing

    As part of a Griffiths problem, I have a charged capacitor placed in a uniform magnetic field which points in +x direction. the capacitor plates are parallel to xy planes. Suddenly, the B field starts decreasing in magnitude...what is the direction of the induced E field? It makes most sense...
  24. F

    Spin interaction with B field

    Homework Statement The problem is stated on page 10 and it is number 9. http://panda.unm.edu/pandaweb/graduate/prelims/QM_F11.pdfHomework Equations I know how to write Sy in the z basis for either spin up or down and I have all the spinors.The Attempt at a Solution I tried solving for |ψ(t)> by...
  25. C

    B field inside solenoid as a result of iron rod

    Homework Statement Consider a solenoid with a time varying current and with a coil of wire placed around it. Suppose there is a soft iron rod inside the solenoid. My question is: What happens to the (induced) current in the coil of wire as a result? Homework Equations Faraday, magnetic...
  26. L

    Looking for equation/proof of b field in a solenoid

    Hi guys, I'm looking for an equation and/or proof of the magnetic field produced inside a solenoid with a finite length (hence, it shouldn't just be "muNOT n I." For some reason I can't find a simple proof anywhere. I have no idea where to start. ampere's law obviously doesn't work, and that...
  27. P

    Spin-1/2 Particle in Superposition B Field: Probability and Interactions

    Lets say I have a spin-1/2 particle that is about to enter a non-constant B field. the spin 1/2 particle has a state vector of |\psi>= \frac{|+z>}{\sqrt{2}} + \frac{|-z>}{\sqrt{2}} What if the B field was also in a superposition like |\psi>= \frac{...
  28. J

    Wire loop placed in B field which is decreasing uniformly

    Homework Statement A wire loop of area 2·0×10−4 m2 contains 40 turns, and has a total resistance of 40Ω. The plane of the loop is perpendicular to a uniform magnetic field of magnitude B0. The magnetic field is now turned off such that the flux through the loop drops linearly to zero. A total...
  29. S

    Griffiths Electrodynamics - Chap 5 clarification curl of B field

    Homework Statement This question is regarding clarifying some reading in Griffith’s Electrodynamics, page 224. “deriving the curl of B” In particular it’s less on electrodynamics and more on some vectors or vector calculus. The book states: we must check that the second term integrates to...
  30. C

    Quick question about acceleration caused by B field

    I know that the magnetic force is calculated via ##\underline{F} = q( \underline{v} \times \underline{B})##. Consider a particle with a velocity at some angle to a constant B field, both v and B in the same plane. Then the force will be acting in/out of the page depending on their orientation...
  31. S

    Griffiths - example 5.5 Electrodynamics - Calculate B Field

    Homework Statement Greetings, In Griffiths, Introduction to Electrodynamics, example 5.5 (page 216), calculating the B field a distance “S” away from a current carrying wire. l' (dl’) is the horizontal current carry wire – will be segmented to dl’ tan(\theta) = \frac{l’}{s} In the next...
  32. N

    Understanding Precession in B Field: Torque and Electron Motion Explained

    There is a problem about precession in general that I am trying to understand, and it can be exampled by electron orbiting around nucleus in external \vec{B} field. We could consider electron motion as loop current which is characterized by the magnetic moment \vec{μ}...
  33. M

    Torque on a rotating solid conducting cylinder in B field

    Homework Statement panofsky 10.3 Find the torque on a solid conducting cylinder rotating slowly in a uniform magnetic field perpendicular to the axis of the cylinder. The Attempt at a Solution let the radius of cylinder r, and the conductivity is σ, the rotating angular...
  34. B

    Comparing Current, Force, B Field, Magnetism

    Homework Statement Please see the attachment and see where i went wrong... simple T/F questions Homework Equations The Attempt at a Solution Here's what i tried 1. T (Right hand rule for both I1 and I2 where I2=-I1 2. F (Since I2 has no current, there is no B field from I2...
  35. H

    Kinetic Energy in B field (is it really conserved)

    Here is a quote from one of the MIT notes on magnetism : "Note that F(magnetic force) is perpendicular to v and B , and cannot change the particle’s speed v (and thus the kinetic energy). In other words, magnetic force cannot speed up or slow down a charged particle. " How is this...
  36. T

    Can Coherent E and B Fields Produce Visible Light in a Box?

    Ok so I was wondering, let's say I have a device (eg., shaped like a toothpaste box with the two square ends cut off). I make 2 of the opposite faces from copper plate and the other 2 from iron plate (for example). I then generate an electric field in the box with the copper plates, and a...
  37. D

    B Field Confinement for Toroidal Coils Driven by AC Current

    It is said that toroidal inductors/coils (see http://fa.tu-sofia.bg/te/Brandisky/images/toroidal_coil.jpg ) that are perfectly axially symmetric will completely confine B fields. That is, the B field inside will be nonzero and will circle the toroid, but the B field outside the toroid will be...
  38. B

    Cycloid motion of electron in perpendicular E and B field

    Homework Statement An infinite metal plate occupies the xz-plane. The plate is kept at zero potential. Electrons are liberated from the plate at y = 0. The initial velocity of the electrons is negligible. A uniform magnetic field B is maintained parallel to the plate in the positive z-direction...
  39. A

    B field intensity of 2 parallel wires

    Homework Statement Two long parallel wires are a center-to-center distance of 4.60 cm apart and carry equal anti-parallel currents of 4.40 A. Find the magnetic field intensity at the point P which is equidistant from the wires. (R = 4.00 cm). Homework Equations magnetic field for a...
  40. Z

    Find momentum of particle in B field

    Homework Statement The problem statement is on the attached file. Homework Equations Lorentz force law maybe. The Attempt at a Solution My teacher actually did this, by calculating the radius of the circle that the particle would orbit to find the momentum using the cyclotron...
  41. I

    Is it possible to get rid of the B field entirely?

    Hi, I was wondering if it is possible to use only relativity and the E field to describe the force that a moving charge feels next to a wire with a steady current in it. Is the concept of the B field necessary? It seems like if we transform into the frame of the moving point...
  42. A

    Finding B field within solenoid.

    1. A current balance is constructed to measure the force between a solenoid with n=10000turns per length and a straight wire segment of length l=0.05m inside the solenoid and perpendicular to the field. The current through both the solenoid and wire segment is I=14A. What is the B field inside...
  43. S

    Force & B Field: Net Force when Test Charge Moves Relative to Current

    I am posting this after seeing this thread: https://www.physicsforums.com/showthread.php?t=592975 and after having thought of the matter for a while, it makes no sense. Have a test charge placed near a wire, and have that wire have electrons flowing in one direction. The protons are...
  44. C

    Electric Dipole in B Field: No Torque

    If i have an electric dipole in a B field, it won't experience a torque right. Because the electric dipole is not moving. So it should just stay put. Just want to check my understanding.
  45. V

    Finding the B field in a long cylindrical hole in a long wire

    So, I'm trying this problem and just want to make sure my attack is correct. We have an infinitely long cylindrical hole in an infinitely long cylindrical wire, like in this picture: (Here, they call the radius of the hole 'a'. I'm going to call it r.) There's an electric current I in...
  46. J

    What are the energy states of a hydrogen atom in a B field?

    If a a 1s hydrogen atom is placed in a B field, how many energy states will it split into?
  47. C

    Do non-inertial frames perceive a B field?

    Lets say I am standing in the middle of a charged ring. And I am standing on a turn table. Now I start to rotate in the center. From my point of view do I perceive a B field. I mean I would have a velocity component.
  48. J

    Find time dependent torque needed to turn a wire loop in a uniform B field

    Homework Statement a single loop of wire with radius A is rotating in a uniform magnetic field at angular frequency ω. The loop of wire drives a current through a resistor R. Determine the torque as a function of time needed to turn the wire. Homework Equations 1) Emf = ∫Fmag.dl...
  49. M

    Motion of wire in B field -vs- motion of electrons in helmholtz coils

    Hi guys, This may be a daft question (or set of questions), but I just want to bounce a few ideas off the wall once I understand some simple issues. Can anyone tell me why if you pass a current through a wire in a magnetic field, the wire will move perpendicular to the both the current...
  50. D

    Rod ontop two parallel influenced by B field

    Hey, I've just been studying for my physics exam in a few days time and I'm trying to work out this problem, a)the proof was straight forward and I wrote that the field is uniform over the cylinder because of cylindrical symmetry and c) I think was ok F = q(vxB) so q|v||B| going up the page...
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