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Understanding the Right-Hand Rule and Cross Product in Magnetism

This overview covers key concepts from Week 5 of PHYS 221 relating to the Right-Hand Rule, the cross product, and magnetic fields. It explains how the cross product is perpendicular to both vectors involved and the geometric interpretation using the Right-Hand Rule. Additionally, it discusses the properties of the cross product, including anti-commutativity and bilinearity. Key applications such as the Lorentz Force and the behavior of magnetic fields generated by moving charges are highlighted. Students are reminded of the importance of contextual understanding in applying relevant formulas correctly.

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Understanding the Right-Hand Rule and Cross Product in Magnetism

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Presentation Transcript

  1. PHYS 221 Recitation Kevin Ralphs Week 5

  2. Overview • HW Questions • Right-Hand Rule • Warning • Magnetic Fields

  3. HW Questions Ask Away…

  4. Right-Hand Rule and the Cross Product • Cross product is perpendicularto BOTH of the vectors in theproduct • You sweep your hand from thefirst vector to the second throughthe smallest angle between • Measures how perpendiculartwo vectors are

  5. Right-Hand Rule and the Cross Product • It’s also possible to do these calculation algebraically, if you are given the vectors by knowing some basic properties of the cross-product (no right-hand rule needed!!!) • Anti-Commutative: • Bilinear: ) • Cyclical in our Cartesian basis vectors:

  6. Warning • There are multiple equations in this chapter that have • It is CRUCIAL that you understand which situations each equation is for so you don’t misapply them

  7. Magnetic Fields • Source • Moving Charges • This is true even for permanent magnets • Shape • Always form closed loops: this means there is no magnetic charge • Always curl around the direction charges are moving in a right-handed way for positive charges • Negative charges reverse the direction of the field

  8. Magnetic Fields • Lorentz Force • What does it tell me? • The force a charged particle experiences in an electromagnetic field • For a wire this becomes

  9. Magnetic Fields • The magnetic force is always perpendicular to the velocity of a charge • This gives some important results: • Magnetic fields do no work: magnetic forces do not change the speed of a particle, so the kinetic energy is constant ergo no work is done • Magnetic forces cause charges to move in loops or helices

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