Biot savart law Definition and 35 Threads

I have attempted to solve it as follows: Using the Biot-Savart law, I found the flux density at the centre of the smaller coil due to the bigger coil as: $$\frac{\mu_0 I b^2 N_2}{2(a^2 + b^2)^{1.5}}$$ where a is the distance to the coil (10cm), N2 is the number of loops in the larger coil (50)...

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...

$$\nabla \times B(r)=\frac{\mu _0}{4\pi} \int \nabla \times J(r') \times \frac{ (r-r')}{|r-r|^3}dV'$$ 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...

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...

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...

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...

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

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"...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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/...

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...

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...

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}...

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...

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>...

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'...

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...

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...

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...

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...

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...

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...

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...

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}

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

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...

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