1. Lesson 7 Magnetic Fields Magnetic Force on moving charge
Motion of charge in Magnetic Field
Magnetic Force on current carrying conductor
Torque on current carrying loop
Hall Effect
Magnetic Devices 1

2. Magnetic Force
Some metallic objects cause other metallic objects to accelerate
Thus must be producing a force
This force is different to Gravitational Force and Electric Force
Can plot the directions of lines field
By alignment of magnetic dipoles
MAGNETIC FORCE 2

3. Magnetic Field Lines 3

4. Properties of Magnetic Fields
Moving charge (current) is effected
Force proportional
Q and v
FB = 0 if v parallel to Magnetic Field B
FB perpendicular to v and B
FB on positive charge opposite to that on negative charge
FB proportional to Sin of the angle v makes with B
Properties of Magnetic Fields 4

5. Mathematical Expression5

6. Vector Product I ( ) ( ) ( ) Vector Product A = A i + A j + A k B = Bx y z B = B i + B j + B k x y z i j k A A A A A A A B = y z A A A = i - x z j + x y k x y z B B B B B B y z x z x y B B B x y z ( ) ( ) ( ) = A B - A B i - A B - A B j + A B - A B k y z z y x z z x x y y x 6

7. Vector Product II A ´ B = - Þ parallel to ( AB ) Sin q ifÞ
parallel to ( AB )
Sin q if
is perpendicular to
and 7

8. Unit vector products 8

9. Work done by Magnetic Field
Work Done by Magnetic Force on charge dW B = F d s Q v ( ) As
is perpendicular to
and
is parallel to 9

10. Work done by Electric Field
Compare to Electric Force
Work done by Electric Field 10

11. - Implications DK 1 1 = m = vf m vi 2 2 Þ vi = vf i . e .
Thus Kinetic Energy of charge is not changed by FB
Potential Energy is not changed 1 1 - = DK m 2 2 = vf m vi 2 2 Þ vi = vf i . e .
speed is constant under influence of B
but v
can change direction 11

12. SI units 12

13. ò Magnetic Flux [ ] Magnetic Flux FB
For constant magnetic field over flat area B
with area vector A F = B
A=ABcosq B
in general ò F = B d A B
surface [ ] F = Tm 2 = Wb (
Weber ) B 13

14. Right Hand Rule for Magnetic Force14

15. Magnetic Force on Moving ChargeB FB v Q k j i F = Q v B = - Q v j B k B y z i j k = - Qv B j k = - Qv B 1 = - Qv B i y z y z y z 1 15

16. Mathematical expression16

17. Uniform Circular Motion of Charge17

18. Mathematical analysisv 2 F
QvB a = = =
Mathematical analysis c r m m mv 2 Þ =
QvB r mv r =
radius of motion QB v = r w BQ \ w
rad =
angular speed =
angular freqency ( ) s m w BQ f = =
frequency (
cps = Hz ) 2 p 2 p m 1 2 p m T = =
period of the motion . f BQ 18

19. Magnetic Bottles
magnetic bottles 19

20. Magnetic Force on Current
Force on current carrying conductor in
a uniform constant magnetic field : ò b F = I d s = I l B B B a ( )
where l = r - r b a é æ ö ù ds dQ v = = = ( ) = ê dQ dQ s ˆ ç ds ÷ s ˆ
I ds s ˆ
I d s ú ë è ø û dt dt 25

21. Want to find total force on charge as it flows from a to b
Vector Integral I ds b rb
B is constant ra
vector integral a
Current I
Want to find total force on charge as it flows from a to b 22

22. Vector Integral II ds b rb B
rb- ra ra a I 23

23. Vector Integral III
Sum ds 24

24. Magnetic Force on Current Loop IB k j i 26

25. Magnetic Force on Current Loop II
Total Force on Loop
Magnetic Force on Current Loop II 27

26. Torque on Current Loop I B I  k z  j i   y 28

27. Torque on Current Loop II29

28. Torque on Current Loop III30

29. Magnetic Moment t = IAB k t = M ´ B M = I A , where A
Torque on Current Loop in yz plane in
a uniform magnetic field in positive y direction t =
IAB k
In general the torque on a current loop in magnetic field is t = M B M = I A ,
where A
is the area vector of the loop ,
with the orientation given by the current flow . 31

30. A=Ai: Area vector with orientation
Oriented Area Vector I k A j i 32

31. I
Hall Effect
Hall Effect A t vd d FE FB B V - E + 33

32. Mathematical analysis
At Equilibrium
Mathematical analysis F = F E B V E = d F = eE = F = v eB E B d E \ v = d B J I
Remember v = = d ne
neA I E BI BI BI \ = Þ n = = =
neA B
EAe V
Vte
dte d 34

33. can measure vd by measuring the PD V.
Measurement
can measure vd by measuring the PD V. 35

34. Lorentz Force 36