Session 2 c palmer august 26 2013

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Unformatted text preview: 2B - Summer Session 2 - C. Palmer August 26, 2013 31   Electrons have intrinsic spin   It can be one of two values, which are opposite in sign and equal in magnitude.   You may remember that orbitals for electrons can contain up to 2 electrons   If they have different quantum numbers   Different spin   If two electrons with opposite magnetic moments are in the same orbital, then the net magnetic moment is 0. Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 32 In atoms with many unpaired electrons, there can be a large magnetic moment because the unpaired electrons can all have the SAME sign moments. Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 33   The torque aligns the dipole with τ = p×E U = −p⋅E the direction of the electric field as well. Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 34   This is the magnetic analogy to integrating over a charged distribution.   Biot-Savart Law µ0 Ids × r ˆ dB = 2 4π r   Permeability of free space µ0 = 4π × 10 Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 -7 T⋅m A 35   Electric differential   Biot-Savart Law µ0 Ids × r ˆ dB = 2 4π r 1 dq ˆ dE = r 2 4πε 0 r   Permeability of free   Permeability of free space ε 0 = 8.85 × 10 −12 space 2 C 2 N⋅m µ0 = 4π × 10 Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 -7 T⋅m A 36   Lucky in this case   Angle between current and r-hat is always π/2   We can use the normal RHR to determine the field is out of the page at C µ0 Ids × r ˆ dB = 2 4π r Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 37   Lucky in this case   Angle between current and r-hat is always π/2   Also r=R everywhere µ0 I ( Rdθ ) ˆ dB = z 2 4π R µ0 I ˆ = zdθ 4π R Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 38   Integrate µ0 I ˆ B= z ∫ dθ 4π R µ 0 Iφ ˆ = z 4π R µ0 I ˆ BLoop = z 2R Physics 2B - Summer Session 2 - C. Palmer August 26, 2013 39   We can use the RHR here to determine the B-field is pointing outside of the page at distance, R, away. µ0 Ids × r ˆ dB = 2 4π r z x y r R r θ ds=dy y Physics 2B - Summer Session 2 - C. Palmer Current: I to the right August 26, 2013 40   We can use the RHR here to determine the B-field is pointing outside of the page at distance, R, away. µ0 Ids × r µ0 I sin θ dy ˆ ˆ dB = = x 2 2 4π r 4π r z x y r R r θ ds=dy y Physics 2B - Summer Session 2 - C. Palmer Current: I to the right August 26, 2013 41   Using some geometry we can substitute out r, dy. z y x µ0 I sin θ dy ˆ dB = x 2 4π r r R sin (θ ) = sin (π − θ ) = r y cot (π...
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