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Physics for Life Sciences Majors Waves, Electricity, and Magnetism

by: Arvilla Bernhard

Physics for Life Sciences Majors Waves, Electricity, and Magnetism PHYSICS 6B

Marketplace > University of California - Los Angeles > Physics 2 > PHYSICS 6B > Physics for Life Sciences Majors Waves Electricity and Magnetism
Arvilla Bernhard
GPA 3.97


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This 4 page Class Notes was uploaded by Arvilla Bernhard on Friday September 4, 2015. The Class Notes belongs to PHYSICS 6B at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 89 views. For similar materials see /class/177935/physics-6b-university-of-california-los-angeles in Physics 2 at University of California - Los Angeles.


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Date Created: 09/04/15
Notes for Physics 6B Three Related Right Hand Rules 0 Three Rules Many Styles There seem to be three right hand rules RHRs 0 Cross Product RHR 0 Loop RHR 0 Grip RHR There are many styles for applying the rst two rules7 by which I mean that there many ways to use your right hand that yield the same result My favorite style7 which I think is superior to the others7 is what I call the Monkey style 1 Cross Product RHR Let7s perform the right hand rule for the vector cross product a X b First7 whether or not these vectors a and b are located near each other7 imagine translating them so that they originate from the same point7 with their tails touching Preserve their directions when translating 1K Km a Q 2 Figure l Mentally Arrange the Vectors Now cause your hand to take a flat planar form7 with your ngers straight and touching side by side and your thumb out at a 900 angle from your ngers Stick your flat hand in the direction of the rst vector a7 leaving your hand free to rotate around the axis of your forearm Now rotate your flattened hand such that your ngers can bend toward the second vector The direction of the cross product vector C a X b is given by your thumb b aW 1 1 N N Figure 2 Cross Product Right Hand Rule7 Monkey Style Note that a X b is perpendicular to a and perpendicular to b and thus it is also perpendicular to the plane that contains a and b We refer to the unit vector f1 in Section 4 539 n U a c39 a 97 Examples Here are some examples of uses of the Cross Product RHR 0 Relationship between axes the usual right handed coordinate system 2 2 X y o Biot Savart law B due to a current distribution B meLdng f 0 Magnetic force on a point charge Fm qv X B When q is negative7 the force is in the opposite direction of V X B For negative charges7 such as electrons7 you can use a left hand rule to nd the direction of the force 0 Magnetic force on a current carrying segment of wire Fm I 6 X B When I is negative7 the force is in the opposite direction of 6 X B 2 Loop RHR The Loop RHR or Loop Orientation RHR7 relates loop direction with threading of ows through the loop as in Amp ere7s law7 and it relates loop direction with surface area vectors as in Faraday7s law When using Amp ere7s law7 B d5 MOIenm P you draw an imaginary closed loop1 P and decide which direction you plan to orient your line integral of B Once you choose that direction7 you use this right hand rule to determine the signs you will assign to any currents that are encircled by this loop Then you can properly add the currents that contribute to the total encircled current IenC Any currents through the loop are said to thread the loop Put your hand along the loop in the direction you have decided to integrate Your thumb gives the direction for positive contributions So7 referring to the gure below7 we have em 1 12 13 T11 i 12 11 12 A K Vlt I dsi I 39 7 fP gt Figure 3 LoopThreading Right Hand Rule7 Monkey Style 1You can call this loop an Amperian loop just like we called our imaginary closed surfaces Gaussian surfaces when using Gauss7s Law When using Faraday7s law of induction7 dltIgtB dt 7 Eds iBda7 P 0115 3 you draw an imaginary closed loop2 P7 which usually coincides with a wire since you are interested in an induced current in the wire7 and decide which direction you plan to orient your arrow for the induced emf 5 The emf arrow goes in the same direction you perform the line integral of Once you choose that direction7 you must also choose a surface S that is bounded by the loop P The surface can be any surface whatsoever7 so long as it is bounded by P S can be at if P exists in a plane or it can bow outward or bend back and forth Usually7 we pick 5 to be at7 if possible With P7 S7 and a direction along P chosen7 we use this right hand rule to determine the direction of the in nitesimal area vectors da in the surface integral of B This will determine the orientation of the surface S and the sign of the magnetic ux IDB Put your hand along the loop in the direction of the emf arrow Your thumb gives the side of the surface on which the in nitesimal surface area vectors da go 5 which7 in more detail7 is 5 K 1 5 F L 2 s 15 1 j P gt Figure 4 Loop Surface Right Hand Rule7 Monkey Style Examples Here are some examples of uses of the Loop RHR o Amp ere7s law 7 Loop Threading o Faraday7s law of induction 7 Loop Surface 0 Ampere Maxwell law 7 Loop Threading and Loop Surface 0 Kelvin Stokes Curl theorem 7 Loop Surface 2You can call this loop a Faradayan loop similar to the Amperian loop and Gaussian surface 3 Grip RHR The Grip RHR or CurrentCirculation RHR relates the direction of the current in a Wire to the direction of circulation of the magnetic eld around the Wire lmagine grabbing the Wire so that your thumb points in the direction of the current arrow for 1 Your ngers wrap around the Wire and provide a reference direction 13 for circulation around the Wire If the current I is positive then the magnetic eld B circulates in the reference direction If the current I is negative then B circulates in the opposite direction For an in nitely long Wire With current I the magnetic eld B due to the current is 01 37 27T7 7 Where 7 the magnitude of r is the perpendicular distance from the Wire to the location of B I I lt lt d3 Figure 5 Grip Right Hand Rule In addition to guring the Bcirculation direction for a straight Wire you can use the grip RHR to help gure out Which direction the magnetic eld points in more complicated situations For example the grip RHR helps in deciding Which direction the magnetic eld points inside a solenoid


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