# Tag Info

0

The other answers are correct in pointing out that due to your choice of loop you cannot factor $\vec B_3$ out of its integral (because its dot product with $d\vec l$ depends on where you are on the loop). However, the reason that the magnetic field at $P$ is given by $\vec B_1 + \vec B_2$ is because of the symmetry of the problem. These infinite wires ...

1

A method that also applies to AC circuits is to move a magnet all the way through a loop connected to a volt meter and sum up all the measurement over time. (They should sum up to zero although the measurement errors may get in the way of a precise 0.)

7

If I understood your question correctly, then you want a simple experiment to demonstrate that magnetic monopoles cannot exist. The simplest way to explain this to a high schooler would be to actually break a small piece of magnet, and then make the student realize that the poles of the magnet haven't been 'split'; instead, both the pieces contain two poles. ...

2

Both pairs of equations are equivalent. In the first equation have the magnetic flux density $B$, which results from the applied magnetic field $H$, and the magnetization $M$. You can think of the magnetization as the response of the material to the applied field. The magnetization is related to the field strength by $$M = \chi_m H \,.$$ where $\chi_m$ is ...

3

In the language of differential forms, the Maxwell-Lorentz equations are simply $$\begin{eqnarray*}\mathrm{d}\!\star\!F = J/\lambda_0 &\text{,}\quad&\mathrm{d}F = 0\text{,}\end{eqnarray*}$$ where $1/\lambda_0$ is the characteristic impedance of free space, and can be fixed to $1$ in appropriate units. From that point of view, all you need to "move" ...

3

The calculus of forms is already well defined on curved manifolds, so you can use $d$ right off the bat.

0

Well... I must be careful with the notation, first start describing the torus that is horizontal and such that the origin lies inside it: $x_t=\mathrm{sin}\left( \alpha_1\right) \,\left( R+\mathrm{cos}\left( \beta_1\right) \,u\right)$ $y_t= \mathrm{cos}\left( \alpha_1\right) \,\left( R+\mathrm{cos}\left( \beta_1\right) \,u\right)$ $z_t = ... 1 Using Biot Savart or Ampere's Law you will come to the same problem$B$is not defined on the ring. This is the same problem that trying to find the Electric field$E$of a puntual charge just in the point where the charge is placed$1/r²$becomes$\infty$... You need to use the formula for volumes but using the superficial current density$J\$ and ...

Top 50 recent answers are included