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e learning electro physics, Lecture notes of Physics

this book from lecturer its contain about physics electro

Typology: Lecture notes

2022/2023

Uploaded on 11/16/2023

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e Learning :
Magnetostatics III:
Multipole Expansion of the Vector Potential and
Magnetized Materials
KB1714614, ELEKTRODINAMIKA 1
FAKULTAS KEGURUAN DAN ILMU
PENDIDIKAN
UNIVERSITAS SEBELAS MARET (UNS)
SURAKARTA
Pertemuan ke-13 : Rabu, 6 Mei 2020 Pk. 14.10 wib
DR. Suharno, M.Si
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e Learning :

Magnetostatics III:

Multipole Expansion of the Vector Potential and

Magnetized Materials

FAKULTAS KEGURUAN DAN ILMU PENDIDIKAN UNIVERSITAS SEBELAS MARET (UNS) SURAKARTA

Pertemuan ke-13 : Rabu, 6 Mei 2020 Pk. 14.10 wib

DR. Suharno, M.Si

1. Multipole Expansion of the Vector Potential Remember, the idea of a multipole expansion is to write the potential in the form of a power series in 1 𝑟 , where 𝑟 the distance to the point in question (Fig. 5.5 1), if r is sufficiently large, the series will be

Multipole Expansion of the Vector Potential…

Example: Multipole Expansion of the Vector Potential…

Example…

2. The Field of a Magnetized Object

We have discussed two mechanisms that account for this magnetic polarization, (1) paramagnetism (the dipoles associated with the spins of unpaired electrons experience a torque tending to line them up parallel to the field) and (2) diamagnetism (the orbital speed of the electrons is altered in such a way as to change the orbital dipole moment in a direction opposite to the field). Whatever the cause, we describe the state of magnetic polarization by the vector quantity M = magnetic dipole moment per unit volume****. M is called the magnetization; it plays a role analogous to the polarization P in electrostatic.

The Field of a Magnetized Object…

The Field of a Magnetized Object…

Ampere's law in Magnetized Materials…

Exercises/Homework (at paper),

Multipole Expansion of the Vector Potential and Magnetized Materials

A long copper rod of radius 𝑅 carries a uniformly distributed (free) current 𝐼 (Fig. 6.19). Find 𝐻 inside and outside the rod!

Ans : 𝐻 = 𝜇 0 𝐼 2 𝜋𝑠

  1. (^) Find the magnetic dipole moment of the spinning spherical shell in Ex. 5.1 1. Show that for points 𝑟 > 𝑅 the potential is that of a perfect dipole! Ans : 𝑚 = 4 𝜋 3

4 𝑧