magnetism - wordpress.com · 2017-03-28 · magnetism electric currents magnetic fields electric...
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Miss Millie Millie
Magnetism �Electric Currents�
Electriccurrentsproducemagneticfields.Magnetscanexertaforceonacurrentcarryingwire.
Thedirectionoftheforceisalwaysperpendiculartothedirectionofthecurrentandalsoperpendiculartothedirectionofthemagneticfield𝐵!⃗ .
𝐹 = 𝐼𝑙 × 𝐵!⃗ 𝐹 = 𝐼𝑙𝐵 𝑠𝑖𝑛 𝜃 (magnitude)
𝑑�⃗� = 𝐼 𝑑𝑙 × 𝐵!⃗ 𝐵!⃗ → 𝑡𝑒𝑠𝑙𝑎(𝑇) = !!"
!!
�Force on an Electric Charge Moving in a Magnetic Field�
�⃗� = 𝑞�⃗� × 𝐵!⃗
If!�⃗� ⊥ 𝐵!⃗ !then𝐹!"# = 𝑞𝑣𝐵
𝐹 = 0if𝑣isparallelto𝐵
Particleinamagneticfieldwithsomevelocitywillmovewith
centripetalforce;𝐹 = !!!
!= 𝑞𝑣𝐵
Thetime𝑇requiredforaparticleofcharge𝑞movingwithconstantspeed𝑣 tomakeoncircularrevolutioninauniformmagneticfield𝐵!⃗ (⊥ 𝑣) is𝑇 = !!"
!where2𝜋𝑟isthe
circumferenceofitscircularpath.
AHelicalPathThevelocityvectormustbebrokenintoitshorizontalandverticalcomponents.LorentzEquation
�⃗� = 𝑞(𝐸!⃗ + 𝑣 × 𝐵!⃗ )
Magnetic Fields 1. DoNOWORK
𝑑𝑙 = 𝑣𝑑𝑡 → 𝑠𝑚𝑎𝑙𝑙 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑚𝑒𝑛𝑡𝑊 = �⃗� ∙ 𝑑𝑙 = �⃗� ∙ �⃗� 𝑑𝑡 = 𝑞!𝑣×𝐵!⃗ ! ∙ �⃗�𝑑𝑡
(𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟) ∴ 𝑊 = 0
2. Donotchangethekineticenergyofamovingcharge𝑑𝑑𝑡𝑚𝑣!
2 =𝑑𝑑𝑡𝑚2 !𝑣!! + 𝑣!! + 𝑣!!!
=𝑚2 !2𝑣!
𝑑𝑣!𝑑𝑡 + 2𝑣! + 2𝑣!
𝑑𝑣!𝑑𝑡 !
= 𝑚𝑣 ∙𝑑�⃗�𝑑𝑡 = 𝐹 = 𝑞𝑣 ∙ !𝑣×𝐵!⃗ !
�The Hall Effect� IntheHalleffect,movingcharges(𝑒!)inaconductorplacedinamagneticfieldareforcestooneside,producingan𝑒𝑚𝑓betweenthetwosidesoftheconductor.
ℰ! = 𝐸!𝑑 = 𝑣!𝐵𝑑ℰ! = 𝐻𝑎𝑙𝑙 𝑒𝑚𝑓𝐸! = 𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝐹𝑖𝑒𝑙𝑑𝑑 = 𝑤𝑖𝑑𝑡ℎ 𝑜𝑓 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟𝑒 = 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 𝑐ℎ𝑎𝑟𝑔𝑒 = 1.60 ×10!!"𝐶 𝑣! = 𝑑𝑟𝑖𝑓𝑡 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦
Torque + Magnetic Dipole Moment
Torqueonacurrentloopinamagneticfield𝐵!⃗ is
𝜏 = 𝜇 !!!⃗ × 𝐵!⃗ Magneticdipolemomentoftheloopis
𝜇 = 𝑁𝐼𝐴𝑁 = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑜𝑜𝑝𝑠𝐼 = 𝑐𝑢𝑟𝑟𝑒𝑛𝑡𝐴 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡ℎ𝑒 𝑐𝑜𝑖𝑙