So people I have been studying this law for the past one week but I can't seem to understand what it is all about the problem with me is that as long as I don't get the why of sth it becomes quite difficult for me to comprehend.
So in the Roger muncaster they were talking about solenoids and wire so can someone please help a sister to understand what exactly this law is all about?
I want to use B_z = (𝜇₀ I)/(4𝜋) * R/(z² + R²) to derive the Helmholtz coil's magnetic field as shown here. But I thought for the Biot-Savart in the equation, the angle θ' for the cross product I ⨯ r hat = I dl ⨯ r hat = I sinθ' is the angle between the current vector I (or the infinitesimal wire dl) and r hat (the direction where dl is pointing w.r.t. the observer), but in the derivation they have done, they used the angle θ between the z-axis and r hat. So what's going on?
Also, how do I get the on-axis magnetic field shown on the Wikipedia page from the one shown on the HyperPhysics page? There seems to be a 1/(2𝜋) discrepancy between these two.
This is driving me insane. It's been two days since I'm tackling this problem. It's simple as the title says, what is the magnetic field above and under the plane, using Biot-Savart law, you can't use Ampère's law, which is blatantly easy. Using Biot-Savart Law, I was only able to get a qualitative description: assuming cartesian coordinates such that the conducting plane matches the xy-plane, and that the surface current density flows in the positive x-direction, we know the field will be in the positive y-direction for z>0 and in the negative y-direction for z<0. Furthermore, in both cases, the magnitude of the field will be constant. So in practical terms, what I need is the magnitude of the fields, but I don't know how to get it. What do I do?
So I've been learning about the Biot-Savart Law and there seems to be some discrepancies between how I learned it and how I'm seeing it applied. Here is both the actual question and the part that has me confused. This is not a homework question. It's just extra practice to prepare for an exam.
The law states that B = (µI/4π)∫dL sin(ø)/r^(2) where, according to my textbook, ø is the angle between the direction of the current and the radius vector aimed at some point of interest. Now if you look at the image that I made, you'll see that the angle ø used is not that of the current and radius vector but rather the angle between the radius and some line perpendicular to I in the direction of P, which is how the solution solves it.
So I guess my question is why are they choosing that angle if the law states that ø is the angle between I and r?
I was trying to derive B-S law for point charge from Ampere-Maxwell equation assuming dE/dt=0 and integrating along a circular loop od radius R with a moving charge at the center. Solving the loop integral gives B2πR, on the right-hand side we've got: u0(j dot area) =u0*(q/πR²)vπR² (for simplicity lets assume theta = 0). The areas cancel out and we're left with something like:
B = u0qv/2πR
Od course there shouldn't be 2πR² but 4πR² in the denominator, so what the hell? I can't really figure out why this shouldn't be true.
Thanks im advance.
Actually, I'm more stuck on cosines and sines than the biot savart law.
Context: Using the biot savart law, I am to calculate the magnetic field at point L, due to two wires, one coming out of the screen and one going in. I've calculated each individual magnetic field to be equal to (mu * I)/(3 pi * d). I then figured, I could make right triangles with hypotenuse d * root3, and then say that each x-component of each magnetic field is equal to the magnetic field times cos theta. (See my work). Apparently I am supposed to multiply by sin theta, but I cannot for the life of me figure out why.
SOS!
The problem: https://imgur.com/a/rs2Uzf0
My attempt at cosines and sines: https://imgur.com/a/P8MQcKQ
I would imagine that at Mines talking about physics is socially acceptable, so I'm asking here.
I am taking a similar course at the school 30 miles away. I just have trouble knowing when it would be more efficient to use the Ampere's Law vs. Biot-Savart. For example, I know that when you have a current going through a rod, you can use Ampere's Law. The magnetic field B encircles the rod, and the vector dl is already parallel to the B field. So B(2pir) = mu_0*I => B = mu_0*T/2pi*r. Ampere's Law takes advantages of symmetries. I've done a problem on a coax cable using AL for an inner conductor of radius a and for the case where r < a.
I wonder what people think of Biot-Savart. In what cases would you use it over Ampere Law? Both of them can find a magnetic field B for a point P away from the object. But it seems like Biot-Savart can be used for cases where there is not a closed loop. For example, if you wanted to find the magnetic field for the origin of a semicircle with no wire connecting the diameter and a current I going clockwise. I am curious to know if there are people here who have a more creative insight on Biot-Savart as it relates to certain geometries.
I have an exam I'd Engineering electromagnetics and I don't know anything, biot savart just doesn't make sense to me because I suck at the basics.
https://www.reddit.com/r/PhysicsStudents/comments/87eq0v/biotsavart_law_integral_help_not_sure_if_there_is/?st=JF917WQP&sh=3ad1646d
https://session.masteringphysics.com/problemAsset/1385104/9/knight_Figure_32_14.jpg
I is 6A.
From that picture, I need to get the magnetic field strength at points A, B and C. I actually already have B as 1.2*10^-4 T, but would appreciate an explanation for it anyway.
I assume I use Biot-Savart Law, but I just don't know how to start with it. Where to I plug numbers in?
https://en.wikipedia.org/wiki/Biot–Savart_law
Since magnetic field is just an electric field seen from a moving frame of reference, you'd think that all the rules of electrodynamics could be derived from SR, but I've never seen it done (without using tensors).
im working on some hw and im kinda confused on P.6-5
http://imgur.com/a/hhCJT
there is a picture of the problem and figure, and also the soln manual answer (EDIT: sorry that question one is bad, http://i.imgur.com/GU91Xjl.jpg)
the first part of the manual makes sense, but where i am confused is the part where they take account for the other sides, like when it says B=a_Z (u_0 x I/(4pi))((1/a)cos(alpha_a)+....
if someone could explain that to me that would be appreciated
why are there both sin and cos terms and why is alpha angle not consistence with the inverse length infront of it?
like why 1/b (sin(alpha_a)) and 1/b (cos(alpha_b)) and not just latter term?
thanks in advacne
In my University Physics class we worked a few problems using the Biot-Savart Law to find either the current or the magnetic field of loops and straight wires. A sphere is basically just a bunch of loops of different radius stacked together, so I imagine if I want to find the current of the earth due to its magnetic field, I would use the Biot-Savart Law and perhaps integrate the radius, however I am having trouble applying it.
