What is Biot-savart: Definition and 122 Discussions

In physics, specifically electromagnetism, the Biot–Savart law ( or ) is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb's law in electrostatics. When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.

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  1. Brian Tsai

    I A math confusion in deriving the curl of magnetic field from Biot-Savart

    I am recently reading "Introduction to Electrodynamics, Forth Edition, David J. Griffiths " and have a problem with the derive of the curl of a magnetic field from Biot-Savart law. The images of pages (p.232~p233) are in the following: The second term in 5.55(page 233) is 0. I had known...
  2. C

    Integrating Biot-Savart Law at a point

    Why when you integrate the Biot-Savart Law do we not include limits of integration on the left-hand side of the equation (for the differential magnetic field)? Would the lower limit be 0 and the upper limit be B? How would you tell? Many thanks!
  3. A

    Biot-Savart equation for AC current

    The fact that the current changes in time should allow me to take it outside from the integral along the coil, since it is not a function of space. But I'm not sure about this assumption, is there something I'm missing or am i correct? Thanks
  4. MarkTheQuark

    I Biological examples of a Biot-Savart law in magnetostatics?

    Hello everyone, So, I was wondering, the Biot-savart show us a magnetic field created by a constant electric current. Initially I thought that an example would be biological systems with a nervous system that works on the basis of electrical discharges, but I don't think it's a valid example...
  5. guyvsdcsniper

    Different forms of Biot-Savart Law

    My book never references the Biot-Savart law with in terms of 1/r^3, only 1/r^2. How is it that it can be expressed as 1/r^3 as well
  6. Z

    Ampere's Law & Biot-Savart: Dealing with Infinity

    How to lose surface integral in derivation of ampere law from biot-savart law if current goes to infinity? How does current that goes to infinity obey Helmholtz theorem for vector fields?
  7. A

    Understanding a step in a Biot-Savart law problem

    I can't understand intuitively why the authors of the book expressed the cross product between the vectors dl and r (unit vector) as: dl sin(pi/2 - theta); isn't it supposed to be expressed as: dl sin(theta)?? So why did the authors put that pi/2 into the argument of sin function, that's my...
  8. HAgdn

    Validating a Modified Biot-Savart Law

    I tried validating the equation by somehow 'solving' only with the involved units. Magnetic Flux Density – Tesla (T) – Weber (Wb) per square meter (Wb/m2)
  9. D

    How to find the magnetic field and magnetic force due to a solenoid loop

    I'm not so sure how to begin with this problem. I was thinking of usign superposition. I think that the field on the conductor due to the parallel segments of the coil is zero, since Ampere's Law tells us that the field outside the solenoid is zero, right? For the perpendicular segments, I used...
  10. J

    Biot-Savart for finite volume currents (Wangsness)

    Since ##\vec{R}/R^3 = -\nabla(\frac{1}{R}) = \nabla^\prime(\frac{1}{R})##, the standard form of the Biot-Savart law for volume currents can be re-written as: $$\frac{\mu_0}{4\pi}\int\limits_{V^\prime}\frac{\vec{J}^\prime (\vec{r}^\prime)\times\vec{R}}{R^3}d\tau^\prime =...
  11. T

    I Relativistic form of the displacement current using the Biot-Savart Law

    The Biot-Savart law which describes a magnetic field created by a displacement current: $$\frac{dB}{dV}=\frac{\mu_0\epsilon_0}{4\pi}\frac{\frac{∂E}{∂t}×r}{r^2}$$ What's the relativistically co-variant form of this equation? Is the introduction of speed of light propagation delays enough, or...
  12. S

    I Analog to Biot-Savart for E field

    On page 317 of "INTRODUCTION TO ELECTRODYNAMICS" 4th Ed. by Griffiths he states without proof that the analog to Biot-Savart for finding the E field is: Can anyone direct me to a reference where this is proved or give me a hint how to prove it? Thank you.
  13. Tomi Kolawole

    Finding the Magnetic Field of a Point Charge Using Biot-Savart Law

    Homework Statement Homework Equations [/B]The Attempt at a Solution I soled for the integral of the magnetic field but i don't know what bounds to intergrate over and also i what is DS in this case? its a point charge so shouldn't bio savart have q(v*b) instead of i(ds*r)?[/B]
  14. Ignitia

    Biot-Savart Law with two semi-circles

    Homework Statement The accompanying figure shows a current loop consisting of two concentric circular arcs and two perpendicular radial lines. Determine the magnetic field at point P. Homework Equations B = μ/(4π) ∫ (I*dl x r)/r2 Btot = Ba - Bb The Attempt at a Solution For part a: Ba =...
  15. Ignitia

    Biot-Savart Law For Calculating Net Magnetic Field

    Homework Statement Two long wires, one of which has a semicircular bend of radius R, are positioned as shown in the accompanying figure. If both wires carry a current I, how far apart must their parallel sections be so that the net magnetic field at P is zero? Does the current in the straight...
  16. C

    Application of Biot-Savart Law for Finite Wire: Exploring Point P and P_1

    Hi, I've got a question regarding application of the Biot-savart law along finite wire. There is a great explenation of this problem in the MIT paper but this does not cover one case. 1. Homework Statement My question is: does the equation defining magnetic field in point P(x,y) also applies...
  17. M

    Magnetic field of a finite wire increasing with distance?

    I am computing magnetic field around a thick conductor to do railgun force modeling. I am currently re-examining my magnetic field computation, and I have found some confusing results stemming from a fairly simple use of the Biot-Savart Law. The main issue is that the more nuanced application of...
  18. M

    Magnetic Field Computation from Thick Rectangular Conductor

    Hello, and thanks in advance for taking a look at my question. Generally, I am trying to make a railgun force model. Since railguns depend on the magnetic field created around the rails (and the resulting Lorentz force) I need to model the magnetic field created by the current that flows...
  19. Eri ep

    I Differentiating Biot-Savart Law

    Hello! I have the equation FM = qvBsinθ . As the end result, I am trying to figure out what B I need to change θ even a little bit. To do that, I was planning to find the minimum B by differentiating B=(μe/4π)(qv x R / R3) in terms of R and setting it equal to zero. . I am assuming that this...
  20. J

    I Explanation of Biot-Savart Law

    I've learned that in a wire with a current flowing through it, a magnetic field is produced, and that to determine the direction of the fields, one could match their thumb with the direction of current and curl their fingers around the wire as shown in the link below. I also learned that in Biot...
  21. PhiowPhi

    The difference between Ampere's law & Biot-Savart Law

    When considering the magnitude of the magnetic field at a certain point (##P##) away from an infinite/finite wire, I can't understand how an infinite wire would generate a stronger magnetic field (##B##) in contrast to a finite wire that has the same dimensions and current applied, at the same...
  22. C

    I How Does the Biot-Savart Law Apply to Angles in an Infinite Wire Calculation?

    In using the Biot-Savart Law for an finite wire, I am having trouble understanding the angles. I have sintheta1-sintheta2, where theta1 is measured from point P to the horizontal wire and from the vertical axis, to the left of point P. Theta 2 is measured to the right of point P. I am ok until...
  23. RoboNerd

    Question on magnetic fields from wire

    Homework Statement Homework Equations Biot-Savart's law and ampere's law expressing B = mu0 * I / (2 * pi * r) The Attempt at a Solution [/B] I know that for the first drawing, we have magnetic fields going into the page from both of the wires, and we have them being (infinitely) long, so...
  24. H

    Why Are Multiple Pressure-Velocity Coupling Algorithms Used in ANSYS Fluent?

    In Fluent, there are several 'pressure-velocity coupling' algorithms. Why are these necessary when, in many fluid mechanics textbooks, it is proposed that for incompressible fluids, an equation for Pressure can be found by taking the divergence of the Navier-Stokes equation, and inverting using...
  25. oogleshmoogle

    When do I use Biot-Savart Law vs. Ampere's Law?

    This isn't a homework problem, I have the solutions for this problem. I'm just wondering why, for question 3, letter a, part ii, it's necessary to use the Biot-Savart law instead of Ampere's law? What are the use cases for Biot-Savart law vs. Ampere's law...
  26. A

    Biot-Savart Law: infinity wire

    Hey! 1. Homework Statement One must simply calculate the magnetic field at a distance s to the wire, which carries a steady current I Homework Equations Should I write the point vector as: \mathbf{r} = s\hat{s} + \phi \hat{\phi} + z \hat{z} or \mathbf{r} = s\hat{s} + z \hat{z} ? The Attempt...
  27. S

    Magnetic field strength for circular loop

    When deriving the magnetic field strength due to a circular loop at some distance away from it's center (using Biot-Savart's law), why is the angle between ds and r 90 degrees? This is a youtube video with the derivation, see 5:55
  28. T

    The Conditions for Biot-Savart Law to Ampere's Law

    Mathematically, what conditions must a B-field that obeys the Biot-Savart Law satisfy before it will obey Ampere's Law? Additionally, what conditions must the B-field obey in order to satisfy Faraday's Law?
  29. S

    Biot-Savart's Law for cylindrical conductor

    Homework Statement The figure shows a cross section across a diameter of a long cylindrical conductor of radius a = 2.92 cm carrying uniform current 151 A. What is the magnitude of the current's magnetic field at the center of the conductor? Homework Equations Biot-Savart's Law The Attempt...
  30. S

    How Does Biot-Savart Law Calculate Magnetic Field at Point P?

    Homework Statement The figure shows two very long straight wires (in cross section) that each carry a current of 3.19 A directly out of the page. Distance d1 = 6.00 m and distance d2 = 4.00 m. What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to...
  31. kenok1216

    Question about Biot-Savart Law (B-field)

    Homework Statement I=10A,L=0.5m,a=0.3m,x=0.2m Homework Equations The Attempt at a Solution by the Biot-Savart Law ds cross r=-dxcosθ k(direction k) dB= μI/4π∫-dxcosθ/r^2 B=μI/4π∫-dxcosθ/r^2 (from ?? to ??) in magnitude question: 1) what is ?? to ?? 2)how dx and r respect to dθ? [/B]
  32. LeoPedranjo

    Trouble with Biot-Savart Law: Instant Effects & Ampere-Maxwell Law

    Guys, I'm having trouble with some concepts on the Biot-Savart Law. Lots of texts compare this law with Coulomb Law, but doesn't affirm that B-S is only applicable on a static case (constant current). What are the real physical conditions in which Biot-Savart Law can be directly applied? Does it...
  33. G

    "Biot-Savart" version of Maxwell-Faraday equation?

    Ampere's Law can be derived from the Biot-Savart Law. Faraday's Law is similar to Ampere's Law. Is there a "Biot-Savart equivalent" of Faraday's Law? I imagine it might look something like this: (not taking into account Coulomb's Law)...
  34. DavideGenoa

    Biot-Savart law from Ampère's (with multivariate calculus)

    Let us assume the validity of Ampère's circuital law\oint_{\gamma}\mathbf{B}\cdot d\mathbf{x}=\mu_0 I_{\text{linked}}where ##\mathbf{B}## is the magnetic field, ##\gamma## a closed path linking the current of intensity ##I_{\text{linked}}##. All the derivations of the Biot-Savart law for a...
  35. avikarto

    LH vs Gaussian units in Biot-Savart Law

    I have a question regarding the relationship between the Biot-Savart formula in Gaussian and Lorentz-Heaviside units. In Gaussian, we have a ##\frac{1}{c}## outside the integral, but in LH units we have a ##\frac{1}{4\pi}\frac{1}{c}##. This does not make sense, considering the transformation...
  36. P

    What is the B-field at the center of a semicircle using the Biot-Savart Law?

    Homework Statement Use the Biot-Savart Law to find the magnetic field strength at the center of the semicircle in fig 35.53 Homework Equations Bcurrent=(μ/4π)*(IΔsXr^)/r2 Bwire=μI/2πd The Attempt at a Solution The solution from the back of the book is B=μI/4πd It looks like they just added...
  37. D

    Why is the curl of Biot-Savart Law equal to zero?

    My understanding of the curl of a vector field is the amount of circulation per unit area with a direction normal to the area. For the vector field described as \textbf{B} =\boldsymbol{\hat\phi} \frac{\mu_{0}I}{2 \pi r} I figured the curl would be something more like this, because it points in...
  38. Nathanael

    Biot-Savart law and Ampere's law

    If we integrate the magnetic field from the Biot-Savart law for an infinitely long straight wire, we can get ##|B|=\frac{\mu_0 i}{2\pi R}## with R being the shortest distance from the wire to the point in space. If we use Ampere's law (with a circle of radius R centered on a wire with the...
  39. T

    Biot-Savart Law method problem

    Homework Statement Homework Equations dB = (μI/4π)(dLsinθ/r^2) The Attempt at a Solution the flat edges of the loop will not contribute to the magnetic field because sinθ = . Only the curved outer loop with radius I will call r2 and length L2 and inner loop with radius r1 and length L1...
  40. 3

    Calculating magnetic flux density using Biot-Savart law.

    Hello, all. I have been working on the following problem and was wondering if someone could check my work and provide some valuable input: Here is my work: What do you guys think about my approach to this problem?
  41. P

    Troubleshooting the Biot-Savart Law for a Circular Loop and Helmholtz Coil Setup

    Homework Statement there is no problem really this is not homework its just something I wanted to include in my lab report. the lab was working with the Helmholtz coil. I was trying to come up with the magnetic field at a distance, Z, from the center of a circular loop of radius, R, that has a...
  42. R

    Applying the Biot-Savart Law to solenoids

    Not really homework but I figured this was the best place to post anyway. 1. Homework Statement I want to find the magnetic field B for an arbitrary solenoid using the Biot-Savart Law. I can find it easily through Ampere's Law, but I'd like mastery over the Biot-Savart Law. Homework Equations...
  43. S

    Is Biot-Savart inverse cube or inverse square law?

    I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...
  44. T

    Biot-Savart non-textbook Equation -- B at point above a loop but off-axis

    I read everywhere about the formulas for calculating B at a point from a length of straight wire, or at a point from the centre of a closed loop. But what about at a point over a closed loop that wasn't the centre? Is there a simple calculation for that? Thanks
  45. T

    Understanding Tokamak Heating: Exploring Maxwell's Equations and Magnetic Fields

    HI, Some things I want to confirm, somethings I need to be reminded of: So what I remember is that Magnetostatics - stationary charges Electrostatics - constant or slow moving charges And that an accelerating charge makes a magnetic field, but you need a time varying field to move charges. So...
  46. H

    Biot-Savart for current density in a volume

    Homework Statement The Biot-Savart law for a current density j in a volume V is: d\vec{B} = \frac{\mu_0\vec{j}\times\vec{r}}{4\pi r^3} dV Derive the formula for the magnetic field created by a single point-like particle carrying charge q moving with velocity \vec{v}. Explain and justify all...
  47. C

    Non-differential Form of Biot-Savart Law: Comparison and Confusion Clarified

    What is the non-differential form of the Biot-Savart law? Is it: B=mi*I/(4R*pi)*(cos(a)-cos(b)) or B=mi*I/(4R*pi)*(cos(a)+cos(b))? For a infinitely long conductor, the law is: B=mi*I/(2R*pi) because a=0 and b=pi. So I would say that the correct expression is the one where the cos are...
  48. S

    Ampere & Biot-Savart: 2 Questions Answered

    I have 2 questions about those 2 equations. 1-) Which one came first in the history of electromagnetism? Some articles say: Biot-Savart derived their equation from Ampere's Law. Some say: Ampere derived from Biot-Savart. Which one is true? 2-) Since Ampere is special form of Biot-Savart and...
  49. W

    Derive Ampere's law from Biot-Savart law?

    In Serway physics, ampere derived Ampere's law(integral B dot ds=uI) with work done on the magnetic charge by magnetic field.(similear with E dot ds) Without using vector calculus, how can derive Ampere's law from Biot-Savart law?
  50. T

    Magnetic field of bent wire for a point along parallel axis

    Homework Statement Long wire is bent such that it forms two parallel line segments that goes to -∞ along the z-axis and a semicircle of radius (R). Find magnetic field on Z axis. Homework Equations Biot-Savart Law (μ0/4π) I = ∫ dl' x R/ R^2 where dl' is element of length and R is the unit...
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