Magnetism and Vectors

Transcription

1 Physics 1051 Workshop 5 Magnetism and Vectors

2 Workshop 5 - Contents I. Where do Vector Cross Products Appear? II. Review of What We've Seen Already I. Magnetic Force on a Charge Particle II.Magnetic Force on Current Carrying Wire III. Cross Product I. Unit Vector Notation Method II.Magnitude Angle Method III.A Few Tips IV. Example 2

3 I Where do Vector Cross Products Appear? 3

4 Magnetic Cross Product Magnetic Force Magnetic Field Torque F B =q v d = 0 4 = r F I ds r r 2 F B =I l = =I A 4

5 II Review of What We've Seen Already 5

6 Magnetic Force On a Charge F B =q v Quantity Type SI Unit Vector N F B q is magnetic force due to magnetic field is charge on charge object (include sign!) v is velocity vector of object is magnetic field [B]=Tesla=Ns/Cm 6

7 Magnetic Force on a Current Carrying Wire F B =I l Quantity Type SI Unit Vector N F B I l is magnetic force on a wire due magnetic field is current in the wire is length vector of object (points in direction of current) is magnetic field [B]=Tesla=Ns/Cm 7

8 III - Cross Product 8

9 Review of Cross Product There are two methods Unit Vector Notation Magnitude Angle Method You will need to be familiar with these methods. With experience some. In the mean time, there are some tips or suggestions that might help... 9

10 Cross Product - Unit Vector Notation Method The steps for this method are Write both vectors in unit vector notation May require finding components Multiply Using Distributive Law Use known information about cross product of the unit vectors A A= A x i A y j A z k =B x i y j z k C= A i i=0 i j= k i k = j j i= k j j=0 j k= i k i = j k j= i k k=0 10

11 Cross Product - Magnitude Angle Method The steps for this method are A Find magnitude of both vectors and angle between them Might need to find angle Might need to find magnitudes Find magnitude using magnitude formula C= A B sin Find direction using right and rule A B C z Still need to specify as angle from coordinate axes. x A y 11

12 Magnitude Angle Method - Right Hand Rule This applies to finding the direction for the result of the cross product between any two vectors. With open palm and thumb off at right angle, point your fingers along first vector Rotate your wrist until hand is oriented such that when you curl fingers they can point along second vector Thumb points in direction of resultant C= A x z C A 12 y

13 Tips for Choosing Method for Finding Cross Product Use Magnitude Angle Method If both vectors are in the same Cartesian plane. Direction can easily be found/specified as unit vector perpendicular from that plane. Possibly if you are given magnitude of both vectors and angle between Use Unit Vector Notation Example x C z z I y Basically any other time Example x A 13 y

14 IV - Example 14

15 Simple Example A Vertical Line of Charge A wire in the figure has a current of 4.0 A. One segment is vertical and of length 0.05 m. The other makes an angle of 10º with the horizontal and has a length of 2.5 m. If it is in a uniform magnetic field of magnitude 0.08 T, what is the total magnetic force on the wire? I 15