What is Biot savart law: Definition and 34 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. T

    I Does B=0 at points out of the plane containing and normal to a point current I?

    Consider a point current I flowing at origin in the positive z direction. Biot Savart Law states that B field must move in an anticlockwise circle everywhere with the infinite line that the direction vector of the current, in this case the z axis, at the center. And its strength must be equal at...
  2. G

    I Deriving Curl of B from Biot-Savart Law & Vector Identity

    $$\nabla \times B(r)=\frac{\mu _0}{4\pi} \int \nabla \times J(r') \times \frac{ (r-r')}{|r-r|^3}dV'$$ using the vector identity: $$\nabla \times (A \times B) = (B \cdot \nabla)A - B(\nabla \cdot A) - (A \cdot \nabla )B + A(\nabla \cdot B)$$ ##A=J## and ##B=\frac{r-r'}{|r-r'|^3}## since...
  3. Elder1994

    Magnetic field due to the current flowing in a bent wire

    Hello, in this problem I'm supposed to calculate de magnetic field due to a bent wire at any point of the x-axis after the bending of the wires. It is obvious that the part of the wire that is parallel to the x-axis makes no contribution to the field so we can focus on the other part of the...
  4. 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...
  5. 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...
  6. jdou86

    Can someone please explain to me how the Biot Savart law is derived?

    Problem Statement: Precised to its constant . Thank you! Relevant Equations: Below En
  7. B

    Biot Savart Law with Different Magnetic Permeabilities

    I would like to make a program that produces a 2D heat map showing the magnitude of the magnetic field produced by a finite length solenoid. The heat map would show the field strength along the radial and axial directions of the solenoid. I plan to divide the conductor into "infinitessimally"...
  8. digogalvao

    Slowly oscillating surface current on a solenoid

    Homework Statement From an original surface current ##\vec{K}=K\hat{\phi}## on a finite solenoid, I got ##\vec{B}=\mu_{0}Kf(z)\hat{k}##, for ##r<R##. Assuming that ##\vec{K}## now slowly oscillates in time such as: ##\vec{K(t)}=K_{0}\cos\left(\omega t\right)\hat{\phi}##, so that I still can use...
  9. C

    What is the last step in the derivation of the Biot Savart Law?

    Homework Statement Hi, So I'm having some trouble deriving the biot savart Law. We have been given a derivation in the notes and I understand everything up until the last step which is labelled in the picture? Equating the two, How did the B vector turn into dB? It seems like he...
  10. Conductivity

    Derivation of magnetic field of a Solenoid: Biot savart law

    Hello, I have seen that biot savart's law works for infinitely narrow wires: "The formulations given above work well when the current can be approximated as running through an infinitely-narrow wire." When I wanted to derive the magnetic field of a solenoid, I had to do this substitution...
  11. A

    Magnetic field of off center triangle - Biot Savart Law

    PICTURE INCLUDED 1. Homework Statement A piece of wire is bent into an isosceles right triangle whose shorter sides have length a The wire carries current I. Calculate the magnetic field for point P. Point P is located on the Y-axis ( 0, √2a). Two corners of the triangle are are located at...
  12. peroAlex

    B-Field on Axis of Equilateral Triangle

    Homework Statement I came across a pretty interesting question that asks for magnetic flux density (B-field) on the axis of the equilateral triangle. This axis is meant to be perpendicular to triangle's surface passing through its centroid. Assuming that a triangle has sides denoted ##a## and...
  13. 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...
  14. T

    Magnetic field behind “invisible barrier”

    Let us consider the following thought experiment. There is a magnetic field in free space produced by a steady current, hence solution of the (magnetostatic) Ampere's law Curl H = J. There is also a material with some parameters ε and μ and no currents, where the Ampere's law is Curl H = 0...
  15. P

    Magnetic field created by a wire acts on the wire itself?

    So here is the problem, it asks me to find the total magnetic field on BA, i made a vectorial sum with the magnetic field generated by i1 and by i2 and i got the right result, but why not adding also the magnetic field generated by the wire itself? I mean generated by CD why isn't that correct...
  16. 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...
  17. M

    What is the formula for a magnetic field due to a finite wire with current?

    Homework Statement A rectangular loop with dimensions 4.20 cm by 9.50 cm carries current I. The current in the loop produces a magnetic field at the center of the loop that has magnitude 3.60×10−5T and direction away from you as you view the plane of the loop. Homework Equations b = mu_0 I L/...
  18. M

    Biot Savart Law Homework Solutions

    Homework Statement A straight wire caries a 10.0−A current (the figure(Figure 1) ). ABCD is a rectangle with point D in the middle of a 1.10−mm segment of the wire and point Cin the wire. Find the magnitude and direction of the magnetic field due to this segment at the following points...

    Use of the Biot Savart Law in Lifting Line theory

    In deriving the lifting line theory Prandtl used the Biot-Savart Law - now from the definition of a vortex filament, it is a line where each point generates a vortex flow in the surrounding fluid. Considering a particular point, if the surrounding fluid is inviscid then shouldn't the vortex...
  20. W

    Magnetic field of a bent wire and Biot Savart law

    Homework Statement A straight wire carrying current I goes down the positive y-axis ( I is also in this direction) from infinite y to the origin. At the origin it changes direction 90 degrees and goes along positive x to infinity. Find B at (0,0,z). I'm given that ##\int_{0}^{\infty}...
  21. R

    What Is the Magnetic Field at Point P Due to a Short Current Element?

    Homework Statement A short current element dl⃗ =(0.500mm)j^carries a current of 8.90A in the same direction asdl⃗ . Point P is located at r⃗ =(−0.730m)i^+(0.390m)k^. Find the magnetic field at P produced by this current element. Enter the x, y, and z components of the magnetic field separated...
  22. C

    Biot Savart Law Calculation problems

    Homework Statement Find the magnetic field from a proton at location r, with velocity v, if the cross-product of vxr is <0,0,6.2e4> and the magnitude of r is 7.34e-2Homework Equations B⃗ =μ/4π * qv x r /r^2 The Attempt at a Solution Substituting in 10^7 for μ/4π 1.6e-19 for q <0,0,6.2e4>...
  23. B

    Question regarding biot savart law and magnetic fields from current

    say you have a very very long (or infinite) straight wire the carried a charge (glued to the wire) and the wire moves forward with speed v with respect to reference frame S, this creates a current, which according to the Biot Savart law creates a magnetic field. But in reference frame S'...
  24. A

    Defining the current vector in the biot savart law?

    I am trying to use the biot savart law to calculate the magnetic field of a given object. I have got to the stage where I have calculated I*dl and R/R^2 separately (doing this in matlab. The problem is where I come to the cross product. If I have a uniform current, the values of the current...
  25. A

    MATLAB How can I improve my MATLAB program for the Biot Savart Law?

    Hi, if anyone good with MATLAB and knows biot savart law then i hope you can help. I have the following program: clear all Img = imread('littlecircle.png'); Img = Img(:,:,1); Img = double(Img); w = size(Img,1); % width size h = size(Img,2); % height...
  26. A

    MATLAB Matlab: help with biot savart law

    Hi, if anyone good with MATLAB and knows biot savart law then i hope you can help. I have the following program: clear all Img = imread('littlecircle.png'); Img = Img(:,:,1); Img = double(Img); w = size(Img,1); % width size h = size(Img,2); % height...
  27. B

    Hertzian dipole consistent with Biot Savart law at small distances

    Homework Statement A Hertzian dipole is located at the origin of spherical coordinates and is aligned with the θ=0 direction. The dipole has strength I(subscript 0)\deltal and oscillates with angular frequency \omega. The magnetic field that it produces is given by the real part of the...
  28. J

    Can the Biot Savart law be used in a medium where the permeability changes?

    Say I use the Biot Savart law to calculate the magnetic field strength at a single point somewhere inside solenoid. I record this value. Then I add an iron sphere to the inside my solenoid very close to but not touching the point just calcuated. If I were to recalcuate the field strength at this...
  29. A

    Ampere's and Biot Savart Law for finite straight conductors

    Are magnetic field lines around a finite current carrying straight conductor concentric circles in plane perpendicular to length of wire? I have seen texts derive an expression for it : B = μ0.i/4πd [cos Φ1-cosΦ2] where d is perpendicular distance of separation of the point...
  30. M

    Solving Biot Savart Law Homework: Infinitely Long Wire

    Homework Statement Using the Biot Savart Law dB = (u0*i*ds X r)/(4*pi*r^3) *X is cross product show that the magnetic field due to an infinitely long straight wire carrying a current i ampere is given by B = (u0*i)/(2*pi*r) Homework Equations Hint: integral...
  31. P

    Why Must the Biot-Savart Law Be a Closed Curve?

    Definition of this law is given by \vec{B}=\frac{\mu_0I}{4\pi}\oint \frac{d\vec{l}\times \vec{r}_0}{r^2} why \oint and no \int. Why must be closed curve? Why not\vec{B}=\frac{\mu_0I}{4\pi}\int \frac{d\vec{l}\times \vec{r}_0}{r^2}
  32. M

    Derivation for Biot Savart Law

    how is the Biot Savart law derived?? From where does it come?
  33. O

    Biot Savart Law with a surface current

    Homework Statement There is a disc with radius R which has a uniformly-distributed total charge Q, rotating with a constant angular velocity w. (a) in a coordinate system arranged so that the disc lies in the xy plane with its center at the origin, and so that the angular momentum point in...
  34. A

    Ampere's Law using the Biot Savart Law

    Is it possible to derive Ampere's Law(circuital) using the Biot Savart Law and elementary calculus? Thanks