1. Magnetic Force Introduction Magnetic force on moving charge Examples
Magnetic deflection animation
x and o diagrams
More examples
Magnetic force on current-carrying wire
Still more examples

2. Magnetism and Induction
Magnetism is weird, both for the force involved and its direction. It’s like a correction to electric forces when charges are in motion, and correction terms are always weird.*
Electric affects charges, magnetism affects charges in motion
Electric causes linear accelerations, magnetism causes sideways deflections (RH rule)
Magnetism and Induction are very, very (societally) important!
Motors, generators, loudspeakers, credit cards, hard drives, transformers…..
*Can derive magnetic force from electric force and Einstein’s theory of relativity

3. Magnetic Force on moving charge
Formal vector definition
𝑭=𝑞𝒗×𝑩
Force Magnitude
𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃
Maximum in v perpendicular to B
Zero when v parallel to B
Like torque, only cares about ⊥ component
Force Direction
Direction right-hand rule
Positive vs. negative charge
B units Tesla = 1 N/A-m (show units)
Units
𝑇𝑒𝑠𝑙𝑎= 𝑁 𝐴∙𝑚 = 𝑁∙𝑠 𝐶∙𝑚

4. Right-hand rule Hand in direction of v Bend in direction B
Thumb points in direction of F
Alternative right hand rules

5. Example - Magnetic Force on moving charge
A proton/electron moves straight north at 105 m/s in a 1 T magnetic field pointed west to east. What is the magnitude and direction of the force?
𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃
= 1.6∙ 10 −19 𝐶 ( 𝑚 𝑠) 1 𝑁 𝑠 𝐶 𝑚 sin(90)
=1.6∙ 10 −14 𝑁
Direction
Proton: straight down into the ground
Electron: straight up in air

6. Example 2 - Magnetic Force on moving charge
It feels no force when its moving in the direction or against the direction of the field (ϴ = 0 or 180). Thus the field must point north to south, or south to north
Direction
v up
B to north
gives F to west
Magnitude
𝐵= 𝐹 𝑞𝑣 = 8∙ 10 −14 (1.6∙ 10 −19 𝐶)(5∙ 𝑚 𝑠 ) =0.1 𝑇 F v

7. Magnetic force video
mp4 video

8. X’s and O’s Simplify diagrams – B field out of or into plane of paper
B coming out B going in
(+) deflects to right (-) deflects to right

9. Circular motion in magnetic field
RHR (flip sign) center of circle
Set mag force = mv2/r
𝑞𝑣𝐵= 𝑚 𝑣 2 𝑟
𝑟= 𝑚𝑣 𝑞𝐵
= (9.1∙ 10 −31 𝑘𝑔)(2∙ 𝑚 𝑠 ) (1.6∙ 10 −19 𝐶)(0.01 𝑁 𝑠 𝐶 𝑚)
=0.011 𝑚 𝑟𝑎𝑑𝑖𝑢𝑠

10. Circular motion in magnetic field

11. Examples – Force on Moving Charge
Problem 11 – Direction of force for (-) charge
Problem 12 – Direction of field for (+) charge

12. Problem Answers

13. More examples – Force on Moving Charge
To accelerate in electric field
𝑞𝑉= 1 2 𝑚 𝑣 2
𝑣= 2𝑞𝑉 𝑚
To deflect in magnetic field
𝑞𝑣𝐵= 𝑚 𝑣 2 𝑟
𝑟= 𝑚𝑣 𝑞𝐵 = 𝑚 𝑞𝐵 2𝑞𝑉 𝑚 = 1 𝐵 2𝑚𝑉 𝑞
Double mass, radius goes up by 2
Quadruple mass, double charge, radius goes up by 2

14. Magnetic Deflection

15. Magnetic Deflection

16. Force on Current-carrying wire
For single charge
𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃
For many charges
𝐹=𝑁𝑞 𝑣𝐵𝑠𝑖𝑛𝜃
Rewriting velocity
𝐹=Nq 𝐿 𝑡 𝐵𝑠𝑖𝑛𝜃= 𝑁𝑞 𝑡 𝐿𝐵𝑠𝑖𝑛𝜃
First term is just current
𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃

17. Summary – 2 magnetic force laws
For single charge
𝐹=𝑞𝑣𝐵𝑠𝑖𝑛𝜃
For current-carrying wire
𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃

18. Example 20-1 𝐹=𝐼𝐿×𝐵 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃 = 30 𝐴 (.12 𝑚) 0.9 𝑁 𝐴 𝑚 𝑠𝑖𝑛60 =2.8 𝑁
= 30 𝐴 (.12 𝑚) 0.9 𝑁 𝐴 𝑚 𝑠𝑖𝑛60
=2.8 𝑁
Direction: into page

19. Example 20-2 3.48∙ 10 −2 𝑁= 0.245 𝐴 (.1 𝑚) 𝐵 𝑠𝑖𝑛90 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛𝜃
𝐵=1.42 𝑁 𝐴 𝑚 =1.42 𝑇
Current direction: CCW
Force on sides

20. Problem 7 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(90) 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(80)
90° w.r.t. field ° w.r.t. field
𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(90) 𝐹=𝐼𝐿𝐵𝑠𝑖𝑛(80)
𝐼= 𝐹 𝐿𝐵 = 6.5∙ 10 −2 𝑁 0.1𝑚 𝑁 𝐴 𝑚 =4.06 𝐴 𝐹= 4.06𝐴 0.1 𝑚 𝑁 𝐴 𝑚 sin⁡(80)
Force: toward viewer =6.4∙ 10 −2 𝑁 toward viewer

21. Magnetron - Microwave ovens
Accelerated radially by radial Electric Field
Spun circularly by crossed magnetic field.
Interacts with resonant cavities around perimeter.
𝐹=𝑞𝑣×𝐵

22. Magnetron - Details
Magnets top and bottom

23. Magnetron - History
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24. Magnetism and Induction Flowchart
law
change
field
Current
force
direct
examples
Force Law 1
B →
qv →
F = qv x B
RHR 1
charge deflection picture tube
Force Law 2
i →
F = il x B
2 wires, motor, loudspeaker
Ampere’s Law
B = μoi/2πr
← i
RHR 2
electromagnet solenoid
Faraday Induction
d/dt →
Φ = B*A →
ε = dΦ/dt i = ε/R
Lentz
generator transformer
Magnetic field plus moving charge/current creates force