What is Biot-savart law: Definition and 84 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. A

    Importance/Use of Gauss' Law and Ampere's Circuital Law

    So the question is like I mentioned. I know how to use GL and ACL in place of CL and BSL. I also know that they make the calculations simpler. The problem is whenever GL and ACL are used in place of CL or BSL, they are used in the following way: Gauss Law:$$\int{ E...
  2. N

    I Resulting magnetic field due to the passage of an AC current

    Hello, Assuming that we have a single-phase electrical transmission line (short distance (< 50 km), stranded, non-isolated, made of aluminum conductor steel reinforced), I would like to know the resulting magnetic field (shape, structure, absolute value, and all other possible details) when...
  3. PhysicsRock

    Magnetic field at origin due to infinite wires and semicircular turn

    Right now, I am trying to calculate the field due to the left straight wire. For clearance, I have oriented the contraption such that the straight wires go from ##z = 0## to ##z = \infty## and pass through ##x = \pm R##, i.e. the semicircle is below the ##x##-axis. The current starts at ##z =...
  4. 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!
  5. 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...
  6. 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
  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. 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...
  10. DJ_Juggernaut

    I Is current in a wire frame-specific?

    There is current flowing in a wire. An observer at rest with respect to current, says there is a magnetic field (B) around wire, due to current, I. [Biot-Savart law]. Now switch to someone moving at the speed of current. The current appears stationary to this someone. Therefore this someone...
  11. 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 =...
  12. 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...
  13. 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...
  14. 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...
  15. 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...
  16. DavideGenoa

    Magnetic field by ideal toroidal solenoid

    I am trying to calculate the magnetic field generated by an ideal toroidal solenoid by using the integral of the Biot-Savart law. I do not intend to use Ampère's circuital law. Let ##I## be the intensity of the current flowing in each of the ##N## loops of the solenoid, which I will consider an...
  17. M

    Magnetic Field at any Point Around a Finite Straight Wire

    Hello, First of all, this question does stem from graduate work, but it seems far too simple to tag "advanced". I am looking to write some code to simulate the force from a railgun. The first step in doing this (from a tutorial I found) is to find the magnetic field at any point within the...
  18. 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...
  19. 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...
  20. 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?
  21. 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]
  22. 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...
  23. 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...
  24. 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...
  25. 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...
  26. 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...
  27. 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...
  28. A

    Biot Savart Law for Charged Particles: Fact or Fiction?

    Well, I am a bit confused. Griffiths himself writes in his book "Introduction to Electrodynamics" at one point in his book that this law is "simply wrong". In a footnote, he writes that it was wrong in principle wheras it is true for non-relativistic speeds, and later on in his book, he goes on...
  29. 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...
  30. 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?
  31. Alex_Neof

    Infinitely long cylindrical shell (magnetic field at centre)

    Homework Statement An infinitely long hollow cylinder of radius (a) carries a constant current (i). Use Biot - Savart's law and show that the magnetic field at the centre of the cylinder is zero. Also show, using symmetry arguments and Ampere's law, the magnetic field is zero in any point...
  32. 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...
  33. 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...
  34. D

    Formula for Helmholtz Coil with a finite thickness?

    The formula for Helmholtz coil is given by mu*(0.8^1.5)*nI/R, where I is the current, n is te number of coil and R is the radius of the coil. Now assume the bunch of coils have a small 'thickness' w (so it looks like a hollow cylinder with a very small height), and the the two coils are...
  35. Hijaz Aslam

    Magnetic Field using Ampere's Law

    I find Ampere's Circuital Law sort of fishy. I don't understand what the actual theory proposes. And the loop that should be taken into consideration adds much to the confusion. How should we select the loop? And in the case of a long wire we find the magnetic field around it by applying...
  36. 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?
  37. F

    Deriving Ampere's law from the Biot-Savart law

    If we write the Biot Savart law as B(r)=μ0/4π∫(J(r')xn/n2)dV' where B is the magnetic field which depends on r=(x,y,z), a fixed point, J is the volume current density depending on r'=(x',y',z'), and n=r-r', a vector from the volume element dV' at r' to the point r. Note we integrate over the...
  38. S

    Is the Biot-Savart Law reversible?

    Please find the attachment and comment about equation (2).
  39. S

    Biot-Savart law and Ampere's law

    1. An electric circuit consists of two long straight sections connecting a loop of radius r. The gap in the loop where the straight sections are connected subtends an angle of theta=60d, as shown in this figure (http://imgur.com/tseDHL6). Determine the magnetic field B at the point P in the...
  40. S

    Magnetic Field, Biot-Savart Law & Current-carrying Wire

    Homework Statement A current I carried in a conduit as described below. The wire can be assumed to be infinitely long in the positive x-direction. The point P is the radius distance a from the portion of the line that describes a semicircle. Calculate the resulting magnetic field at point P...
  41. C

    Question regarding Biot-Savart law

    In my E&M class yesterday, in going over an example for the Biot-Savart law, I couldn't quite understand the initial setup of a problem (this may be more of a math question, but given the source, I figured it ought to be posted here). The attached picture is a crude MS Paint reproduction of the...
  42. C

    Direction of Magnetic Field Outside a Cylindrical Wire

    Hi guys, sorry to bug again, but I am a wee bit stuck. Homework Statement A steady current of 1A flows down an infinitely long straight cylindrical wire of radius r=5mm Explain in what direction the magnetic field is pointing outside the wire Homework Equations The Biot Savart law -...
  43. A

    Biot-savart law question for an infinite sheet

    Homework Statement A filamentary conductor carrying current I in the az direction extends along the entire negative z axis. At z=0 it connects to a copper sheet that fills the x>0,y>0 quadrant of the xy plane. (a) Set up the Biot-Savart law and find H everywhere on the z axis; (b) repeat part...
  44. D

    Derivation of the Biot-Savart Law from Coulomb's Law?

    The title says it all--I'm working through The Feynman Lectures, and came across the assertion that a magnetic field can be thought of as a relativistic-transformation of an electric field (and vice-versa). This makes sense to me, since the magnetic field of a moving point-charge can easily be...
  45. H

    Biot-Savart Law- magnetic field produced by single wire.

    Biot-Savart Law-- magnetic field produced by single wire. Homework Statement A wire of length L, carrying current I lies along the x-axis as shown in the picture. A point P is located a distance 2L below the right end of the wire, as shown. a) Determine the direction of the contribution dB to...
  46. M

    Magnitude of magnetic flux of a solenoid using Biot-Savart law

    Homework Statement A 10 cm long, 1 cm diameter solenoid contains 500 turns of wire. A current that varies as I = 5Sin(100πt) Amps flows through the solenoid wire. Calculate the magnitude of the magnetic flux at the centre of the solenoid as a function of time using equation (1). Compare this...
  47. E

    Understanding the Invariance of dl in Biot-Savart Law

    In the expression of Biot-Savart law B = (µo/4π) ∫ (I dl x r^)/r2 why dl does not depend on the coordinate systems ? in books they are using del X dl = 0
  48. S

    Use of Biot-Savart Law for Square Loop

    Hey, My question concerns the integration of the biot savart law of a differential magnetic field element to find the magnetic field at the center of a square loop. The question is part (c) (using info from (b)) of the image below: I want to check if what I did was right, but what I...
  49. C

    What is the Biot-Savart Law and How is it Used to Calculate Magnetic Fields?

    Homework Statement I have attached a diagram with the question. Homework Equations Biot-Savart law: (μ/4π)(I/r^2)(dlxr) or (μ/4π)(q/r^2)(dvxr) The Attempt at a Solution My question is, The B field can be predicted from the right hand corkscrew rule right? So the part of the...
  50. P

    Biot-Savart Law, right angle

    Homework Statement http://i.minus.com/1333003834/Q661ScjxBUxkrL2FfmVFPQ/iTEfM3UTAVtTa.png Homework Equations B = ∫ ([μ0 / 4pi] * I * ds-vector x r-hat) / r^2 The Attempt at a Solution I know the horizontal line will not add anything to the magnetic field (B), so focusing on...