3. A Brief Recap Charged particles in motion create magnetic fields around themselves. We can use Right-Hand Rule #1 to determine the direction of a magnetic field produced by one or more charged particles in motion. The Principle of Superposition applies to B fields just as it did to E fields.

4. Sketch the magnetic field of a loop of wire from a cross-sectional view. (Imagine a donut cut in half and looked at from the side) Whiteboard Warmup II

5. Use RHR #1 for each section of the loop, and then use the Principle of Superposition!

6. Superposition Whiteboard Two wires carrying equal currents are crossed, as shown above. Determine the magnetic field in each of the labeled regions.

7. B = 0 T

8. B Field of a Current-Carrying Wire μ 0 is a constant called the permeability of free space μ 0 = 1.3 x 10 -6 T * m/A Directly proportional to the current through the wire Drops off hyperbolically with radial distance from wire r

9. 10 cm 6 cm Current Events Two parallel wires are each carrying a current of 0.8 Ampères upward, as shown below. Calculate the magnitude and direction of the magnetic field at points A, B and C shown below. μ 0 = 1.3 x 10 -6 T * m/A 4 cm

10. B A = 2.2 x 10 -6 T out of the page B B = 0 T B C = 3.1 x 10 -6 T out of the page 10 cm 6 cm 4 cm Vector superposition in the third dimension!

11. Magnetic Force Just as charged particles in motion create magnetic fields, charged particles in motion are the only thing that can feel a force exerted by a magnetic field. Moving charged particles create B fields. Other moving charged particles in these B fields can feel a force from the field.

12. Magnetism: It’s All Perpendicular A charged particle moving in a B field will only feel a magnetic force if some component of its velocity is perpendicular to the B field. B v v v Motion perpendicular to B field: Maximum magnetic force Some component of motion perpendicular to B field: Some magnetic force Motion parallel or antiparallel to field: Zero magnetic force

13. Strength of the Magnetic Force B v q θ Depends on four things Magnitude of charge Speed of particle Strength of B field How much of the velocity is perpendicular to the field Angle between v and B If θ = 0° or 180°, F B = 0 N If θ = 90°, F B = qvB

14. Direction of Magnetic Force The magnetic force felt by a particle will be perpendicular to the particle’s velocity, and also perpendicular to the magnetic field. To model this accurately, we need to use another right-hand rule!

15. Right Hand Rule #2 1. First, align your thumb with the direction of the current (flow of positive charge) 2. Then, while keeping your thumb in that direction, twist your right hand so that your fingers align with the B field 3. Your palm will now point in the direction of the magnetic force!

16. RHR #2: It’s fun, 3-D and easy to remember! Thumb: Current Fingers: Field Palm: Push Warning! Make sure that your thumb stays aligned with the current while you are lining up your fingers with the B field.

17. WB: What is the direction of F B ?

18. FBFB FBFB FBFB FBFB

20. Whiteboard: Which way is F B ? v v I a)b)

21. a)B field is into page. Force is upward. b) B field is upward. Force is zero.

22. Negative Charges in B-Fields The force will be in the opposite direction than if the particle were positive. 1.Point your thumb in the direction of the negative particle’s motion 2.Turn your hand to align your fingers with the B-field. 3.The force felt by the negative charge will point away from the back of your hand!

23. Which way will the electron feel a magnetic force? I v

24. B v FBFB Solution

25. For Tomorrow’s Quiz Know how to: 1.Determine the magnitude and direction of a magnetic field formed by a current-carrying wire. 2.Determine the direction of the magnetic field formed by a magnet or loop of current. 3.Determine the magnitude and direction of the magnetic force felt by a positive or negatively charged particle in a magnetic field.