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. B

    Magnetic flux density calculation for high permeability material

    Hi to all of you, As the Biot-Savart-Law is based on experimentations in air, i like to know how to calculate the magnetic flux density in material with much greater permeability, where the circular like shape of the field distribution troughout the vicinity does not apply. Does anyone has a...
  2. M

    Biot-Savart and a Rectangular Loop

    Homework Statement Consider the figure on the right. Wire 1 is oriented along the y-axis and carries a current I1. A rectangular loop located to the right of the wire in the xy-plane carries a current I2. Find the magnetic force exerted by wire 1 on the top wire of length b in the loop...
  3. 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...
  4. S

    Is the Biot-Savart Law reversible?

    Please find the attachment and comment about equation (2).
  5. J

    Magnetic field from a conductor using Law of Biot-Savart

    Homework Statement An electric current I flows in a straight conductor of length L. Use the law of Biot-Savart to find the magnetic field at a point lying on an axis going through the centre of the conductor and perpendicular to the conductor. Homework Equations Law of Biot-Savart...
  6. D

    Ap physics c ampere's law and biot-savart

    For AP Physics C level, I am having trouble on deciding whether to use Ampere's Law or use Biot-Savart. Are there any hints/tricks for deciding what to use? For example, in solenoids i heard it's easiest to use Ampere's Law
  7. 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...
  8. 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...
  9. P

    Physics 2: Electromagnetic Theory (Amperè's Law, Biot-Savart, etc)

    Homework Statement First off: these are not homework problems technically, I'm doing these for my own benefit...they're not being graded or collected. Just trying to study for my final. Problem 1 A thin spherical, conducting metal shell has a radius of 15.0cm. A positive charge of 1.30µC...
  10. 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...
  11. 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 -...
  12. 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...
  13. 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...
  14. 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...
  15. N

    Biot-Savart - Differential Length Element?

    Hi, I'm trying to work with the Biot-Savart law to look at the magnetic field strength along the center of an asymmetric solenoid I wrapped. I parameterized the coils with x = r cos 2(pi)t, y = r sin 2(pi)t, and z = D t where r is the radius of the coil layer, D is the diameter of the wire...
  16. atomqwerty

    Doubt with Ampere and Biot-Savart

    Hello, I think I'm terribly wrong by supossing Ampère-Maxwell and Biot-Savart are referred to the same concept of magnetic field B. For example, for calculating B near an infinite line, I used both, as I understood them, obtaining different expressions (see image). What is that that I don't...
  17. 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...
  18. 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
  19. 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...
  20. 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...
  21. P

    How Does the Biot-Savart Law Apply to a Right Angle Wire Configuration?

    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...
  22. F

    Magnetic Field From a Solenoid - Biot-Savart Law

    I'm fairly confident I can express the strength of a magnetic field along the axis of a current carrying loop at some distance x away using the Biot-Savart Law. I'm just trying to extend this idea for a solenoid with N turns. I'm assuming that the current would become NI in this case? Regards Dan
  23. E

    Biot-Savart law My proof includes a negative sign

    Homework Statement A square coil of wire of side length 2a lies in the yz plane. A current I flows through the loop. The x-axis is defined such that it passes through the centre of the loop, with the loop boundaries being at z±a and y=±a respectively. Given that I flows in a direction...
  24. E

    Calculating Magnetic Field at a Point Using Biot-Savart Law

    Homework Statement A long (effectively infinite) wire segment is connected to a quarter of a circular arc with radius a. The other end of the arc is connected to another long horizontal wire segment. The current is flowing from the top coming down vertically and flows to the right along the...
  25. M

    Biot-Savart law and Poisson's equation

    Dear colleagues, I have questions regarding Biot-Savart law. From [1], it is shown that the equation (Biot-Savart) is derived from the solution to Poisson's equation (assuming here div A=0) \begin{equation} \vec{\nabla}^2 \vec{A} = -\mu \vec{J} \end{equation} which is \begin{equation}...
  26. 0

    What is the Magnetic Field at the Center of a Square Loop Carrying a Current?

    Homework Statement A conductor in the shape of a square of edge length 0.28 m carries a current I = 17.0A. Calculate the magnitude of the magnetic field at the center of the square. Round your answer to three significant figures. Take the permeability of free space to be 4*pi*10^-7...
  27. teroenza

    Ampere's Law vs Biot-Savart arouns a Square

    Homework Statement A conductor in the shape of a square loop of edge length l = 0.360 m carries a current I = 10.0 A. Calculate the magnitude and direction of the magnetic field at the center of the square. Homework Equations ∮B⃗ ⋅dr⃗ =μ0 Ienclosed Ampere's Law B=μ04π ∫I dl⃗ ×rˆr2...
  28. S

    How Does the Biot-Savart Law Apply to Forces Between Wire Segments in a Loop?

    1. A circular loop of wire of radius R = 5.14 m lies in the xy-plane, centered about the origin. The loop is carrying a current of I = 6.91 A flowing in counterclockwise direction. Consider two l = 1.52 mm segments of the loop: one centered about the positive x-axis, the other centered about the...
  29. F

    This question is giving me a headache Biot-Savart'

    Homework Statement The two wires shown below carry currents of 5.00 A in opposite directions and are separated by 10.0 cm. Find the direction and magnitude of the net magnetic field at the following locations. (a) at a point midway between the wires (b) at point P1, 10.0 cm to the right of...
  30. H

    Why is Biot-Savart Law Zero for Cylinderical Uniform Current Density?

    if you want to calculate the magnetic field of a cylinderical uniform current density by Biot-savart law, it will be zero, but by Ampere law it is not zero? why? please guide me
  31. D

    Magnetic Fields and the Biot-Savart Law

    Hi, I'm new here but been looking to you guys for solutions for a while now. However, I cannot find the kind of solution on here already, so I thought I'd put it out here. My main problem with physics is always just finding the formulas I need. If you can at least point me in the right...
  32. D

    Help Understanding Biot-Savart Law Issue

    I've been looking at my electromagnetism lecture notes I have been given and am trying to make sense of a step made in parameterising a current loop. I am really confused about the part where dl is first state. I have no idea how the 0, sine and cosine got there. I suspect that it's something...
  33. A

    What are the differences between Biot-Savart Law and Ampere's Law?

    What is the difference between Biot- Savart Law and Ampere's Law ? both have same result in application . than what is the basic difference between them.
  34. T

    Biot-Savart applied to rectangular coil

    Homework Statement A rectangular current-carrying coil, with side lengths a and b has N turns. The current, I is stable. The coil is shorter than its width. Calculate the magnitude of the magnetic field at the centre of the rectangle. Homework Equations The law of Biot-Savart (I think)...
  35. S

    Electromagnetics = Biot-Savart Law around square path

    Homework Statement Find the B-field at the center of the square loop located above the xy plane, with width (w), and current I rotating counter-clockwise. Homework Equations Here is the given equation: B = [(μo*I*aФ)/(4∏*ρ)](cosα2 – cosα1) The final answer is for the B-field about...
  36. N

    Biot-Savart current loop equation confusion?

    Hello, I am having a bit of a problem with this classic example. I know about the symmetry but I would like to push through the math anyway. The field point is at distance Z from loop on Z axis. Using cylindrical coordinates I am at: dH = I*(rho)d(phi)*a(phi) X (z*az - rho*a(rho)) /...
  37. S

    Using Biot-Savart to solve for B at center of square

    Homework Statement Use the Biot-Savart equation derived in class for a long, straight wire to show that B (at the center of a square with sides L and current I) = \frac{\mu I}{\pi} \frac{2\sqrt{2}}{L} Homework Equations We derived the following in class for a long, straight wire and...
  38. S

    Magnetic fied at center of semicircle Ampere's Law Biot-Savart Law

    Homework Statement A long wire is bent into semicircle of radius R at its center and continues on to infinity in both direcions with the straight segments remaining parallel, as shown in the figure below. Use your knowledge of superposition, Ampere's Law, and the Biot-Savart Law to determine...
  39. D

    Biot-Savart Law for a Point Charge

    Homework Statement Show that B for a point charge is equal to Homework Equations I'm not all that sure. I read that maxwell's equations can be used to derive this, so I'd imagine that it's The Attempt at a Solution If it were that, then, if i have a point charge moving...
  40. 1

    Biot-Savart Law Difficult Problem

    Homework Statement A short, straight wire segment of length l carries current I and is oriented so that it makes an angle of 30° with the horizontal. Point P is a distance r below the wire segment. Which expression below is the best approximation for the magnetic field caused by the wire...
  41. Y

    About the curl of B using Biot-Savart Law

    I am reading the Griffiths about finding the curl of B using Biot-Savart Law. I do not understanding the step between equation (5.52) and (5.53) which finding the x components of the following: (\boldsymbol{J}\cdot\nabla^{\prime})\dfrac{\hat{\xi}}{\xi^{2}} where...
  42. B

    Question on Biot-Savart Law for Finite Length Filamentary Conductor

    When finding the angles for the finite length Biot-Savart formula of a filamentary conductor H = I*(cos(α2) - cos(α1))aΦ/(4πρ), is α1 supposed to be calculated at the start of the current, and α2 at the end? I'm just wondering because my book does it this way and vice-versa, so I'm not entirely...
  43. P

    Biot-Savart Law: Find formula for B at general pt (x, y, z)

    Homework Statement See attachment for Problem Statement. Homework Equations The Attempt at a Solution Can anyone help me start this problem, or clarify what is being asked? I have no idea where to begin.
  44. M

    Solving Biot-Savart Law for a Ring of Charge

    This is a simple problem if you work with only magnitude and consider the symmetry of a ring. However, I am taking a detailed approach, and I am not getting the correct answer. Could you please look over my math? a evenly distributed ring of charge on the positive Y-Z plane has a current, I...
  45. S

    How Does the Biot-Savart Law Apply to a Square Loop in a Plane?

    Homework Statement A square loop of wire C, with side length 2a lies in a plane P and carries a steady electic current I. By using the Biot-Savart law show that the magnetic field B(r) at any point r in P but not in C is perpendicular to the plane P. Calculate the magnetic field at the...
  46. A

    Magnetic Induction at Point on Conductor: Biot-Savart Law

    Homework Statement What is the magnetic induction at a point on a current carrying conductor itself according to biot -savart law? is it zero, infinity? Homework Equations The Attempt at a Solution
  47. A

    Does Biot-Savart law apply at high frequencies?

    The Biot-Savart law for calculating magnetic fields due to a current is presented in my freshman physics book as a general way of getting B from I. But there's no time delay implied by the integral. Can I just manually throw the time delay into the integral? For instance, to numerically...
  48. K

    How Can I Derive the Biot-Savart Law?

    Hi Folks, I have a quick question about the Biot-Savart Law, I know what it is, but I don't know how to derive it. Could anyone give me either links or show me the derivation with origins. I have tried to google it but to no avail. Thanks in advance for all your help in advance Kipper
  49. B

    Expressing Biot-Savart Law using diagram

    Homework Statement Express: in terms of R, L(t), l, and φ Homework Equations Law of Sines and Cosines The Attempt at a Solution I have used: c^2=a^2+b^2-2ab*cosφ which resulted in r^2=R^2+(L(t)-l)^2-2*R*(L(t)-l)*cosφ and used the law of sines to get R*sinφ=r*sinθ...
  50. W

    Magnetic field using the Biot-Savart Law

    Homework Statement A small current element at the origin has a length of 2.0mm and carries a current of 2.0A in the +z direction. Find the magnitude and direction of the magnetic field due to this current element at the point (0,3.0m,4.0m). Homework Equations Biot-Savart Law...
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