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PHYS 241 Recitation

PHYS 241 Recitation. Kevin Ralphs Week 8. Overview. HW Questions Magnetostatics Biot-Savart Law Gauss’s Law for Magnetism Ampere’s Law. HW Questions. Ask Away…. Magnetostatics. Electrostatics vs Magnetostatics

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PHYS 241 Recitation

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  1. PHYS 241 Recitation Kevin Ralphs Week 8

  2. Overview • HW Questions • Magnetostatics • Biot-Savart Law • Gauss’s Law for Magnetism • Ampere’s Law

  3. HW Questions Ask Away…

  4. Magnetostatics • Electrostatics vsMagnetostatics • When we were talking about electrical phenomenon earlier in the course, we assumed we were at an equilibrium so no charges were moving • For our study of magnetism we will assume that our current is steady (or at least not varying rapidly) and that we are not too far away from our magnetic field source • Note that the principle of superposition is valid in both of these approximations

  5. Biot-Savart Law • What does it tell me? • The magnetic field produced by a current in the magnetostatic approximation • Why should I care? • This is a fundamental physical principle derived from experimental data

  6. Biot-Savart Law • The cross product in this equation is important and gives you a lot of information • The cross-product carries all the information about rotations in our 3D space • So the presence of the cross-product tells you that only currents that are flowing AROUND a point contribute to the magnetic field

  7. Biot-Savart Law • When running a Biot-Savart Law integral, it often becomes crucial to draw a picture to make sure you get the cross product correct • FYI: If the magnetostatic approximation fails you would have to use the equation below!

  8. Gauss’s Law for Magnetism • What does it tell me? • The net magnetic flux through a closed surface is zero • If you recall our discussion about electric flux, the net flux of a field through a closed surface is proportional to the total sources and sinks that are within the volume bounded by the surface • This means that there are NO magnetic charges

  9. Gauss’s Law for Magnetism • Why should I care? • Gauss’s law gives you important information about the shape of magnetic field lines • Essentially, magnetic lines of flux are loops and they never converge or diverge on a point Note: when there are no currents flowing, we can use the concept of magnetic “charge” to solve problems, but this is a theoretical tool only

  10. Ampere’s Law • What does it tell me? • A closed path integral of the magnetic field is proportional to the current that flows through the loop • Why should I care? • You can always use it to calculate the current within a region and when there is a HIGH of degree symmetry you can figure out the magnetic field

  11. Ampere’s Law • Although this isn’t called Gauss’s law, this idea functions much like Gauss’s law for electric fields. • This means that all the details about Gauss’s law apply here • You must use a closed loop • The current is that which is enclosed by the loop: this plays the analog as the source of a magnetic field • A line integral is a sum: Just because it evaluates to zero, does not mean that the magnetic field is zero • You must already know something about the magnetic field prior to applying Ampere’s Law

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