1. Magnetic Force
On a moving charge
§21.2

2. Vector Direction Conventions
Right
Left Up
Down In
Out

3. Magnetic Force on a Charge
F = qv  B
Source: Griffith, The Physics of Everyday Phenomena
F is directed out of the screen.

4. Vector Cross Product Operation symbol 
Another way to multiply two vectors
Product is a vector!
Direction of AB is perpendicular to both A and B

5. Cross Product Magnitude
A  B = ab sin q A q
Maximum for q = 90°
Zero for q = 0°, 180° B b

6. Magnitude Geometricallyq B b
AB = area of parallelogram

7. Magnetic Force on a Charge
F = 0 unless charge is moving
F = 0 if velocity is  to field
F = maximum if velocity is  to field
F  0 only if charge crosses B field lines
F = qvB sin(q) in general
If v or B reverse, direction of F reverses

8. Group Work
What are the units of magnetic field B?

9. Cross Product Direction
Curl right-hand fingers in direction of q
Right-hand thumb points in direction of cross-product
Not commutative A B a b q
AB = –(BA)

10. Force Direction F = qv  B Right-Hand Rule
SCI340 L46 Lorentz force
Force Direction
F = qv  B qv
Source: Griffith, The Physics of Everyday Phenomena
Right-Hand Rule

11. Origami Right Hand paper square creases: in out vectors fold over
magnetic
field
current qv
Force
Lorenz
vectors
fold over

12. Group Question
What is the direction of the force on the object moving with velocity v through magnetic field B? A. D. B + B. E. v C. F.

13. Group Question
What is the magnitude of the force on object A compared to the magnitude of the force on object B? B A B v q v 2q

14. Group Work
A particle with charge q has a velocity perpendicular to a uniform magnetic field. What will its subsequent path be? B v q

15. Force on a current
§21.5

16. Force on a Current Moving charge Q with speed v in a length L of wire
In time Dt, charges move a distance Dx = vDt
The quantity of charge passing a point in time Dt is DQ = Q Dx/L = QvDt/L
The current is I = DQ/Dt = Qv/L
Qv = IL

17. Force on a Wire
Qv = IL
So F = Qv  B = IL  B

18. Group Question
Two parallel wires carrying currents in the same direction
attract each other.
repel each other.
have no effect on each other.
Think of their magnetic fields and charge movements!

19. Force between parallel currents
SCI340 L46 Lorentz force
Force between parallel currents
What is the force on this current? I  B

20. Force between parallel currents

21. Definition of Ampere If two parallel wires are held 1 m apart,
with currents of 1 A through each wire,
the attractive force between the wires is 2  10–7 N for each meter of length of the wires.

22. Torque on a loop
§21.6

23. Torque on a Current Loop
A parallelogram in a B field
Any orientation I W L
Opposite forces cancel
Torques do not

24. Loop Dipole Moment
Magnitude = m = IA
Direction = right-hand rule I m

25. Effect of Torque
The magnetic field “tries” to orient the current loop so that its magnetic dipole points in the direction of the field.
Just like a dipole magnet in a field
Because that’s what it is