PHY2049_06-27-11 - Chapter 32 Maxwells equations Magnetism...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
6/27/2011 1 Chapter 32 Maxwell’s equations; Magnetism in matter In this chapter we will discuss the following topics: -Gauss’ law for magnetism -The missing term from Ampere’s law added by Maxwell -The magnetic field of the earth -Orbital and spin magnetic moment of the electron -Diamagnetic materials -Paramagnetic materials -Ferromagnetic materials (32 – 1) The magnetic flux through each of five faces of a die (singular of ''dice'') is given by Φ B = ± N Wb, where N (= 1 to 5) is the number of spots on the face. The flux is positive (outward) for N even and negative (inward) for N odd. What is the flux (in Wb) through the sixth face of the die? A.1 B.2 C.3 D.4 E.5 Fig.a Fig.b In electrostatics we saw that positive and negative charges can be separated. This is not the case with magnetic poles, as is shown in the figure. In fig.a we have a p Gauss' Law for the magnetic field ermanent bar magnet with well defined north and south poles. If we attempt to cut the magnet into pieces as is shown in fig.b we do not get isolated north and south poles. Instead new pole faces appear on the newly cut faces of the pieces and the net result is that we end up with three smaller magnets, each of which is a i.e. it has a north and a south pole. This result can be expr magnetic dipole essed as follows: The simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles do not exists as far as we know. (32 – 2) i B r ˆ i n i φ A i 1 2 3 The magnetic flux through a closed surface is determined as follows: First we divide the surface into area element with areas , , ,..., n n A A A A B Magnetic Flux Φ For each element we calculate the magnetic flux through it: cos ˆ Here is the angle between the normal and the magnetic field vectors at the position of the i-th element. The inde i i i i i i i B dA n B φ φ ∆Φ = r 1 1 x runs from 1 to n We then form the sum cos Finally, we take the limit of the sum as The limit of the sum becomes the integral: cos n n i i i i i i B i B dA n BdA B dA φ φ = = ∆Φ = → ∞ Φ = = SI magnetic flux un r r ° ° 2 T m known as the "Weber" (Wb) it : (32 – 3) B B dA Φ = r r ° Gauss' law for the magnetic field can be expressed mathematically as follows: For any closed surface Contrast this with Gauss' law for cos the electric field: 0 B enc E o BdA B dA q E dA ε φ Φ = Φ = = = = r r r r ° ° ° Gauss' law for the magnetic field expresses the fact that there is no such a thing as a " ". The flux of either the electric or the magnetic field through a surface is proportional Φ magnetic charge to the net number of electric or magnetic field lines that either enter or exit the surface. Gauss' law for the magnetic field expresses the fact that the magnetic field lines are closed.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern