Lect09 handout

Lect09 handout

• 1.
  Currents and MagnetismPhysics 102: Lecture 09
• 2.
  Summary of TodayLast time: Magnetic forces on moving charge magnitude F = qvBsin(  ) direction: right-hand-rule Today: Magnetic forces on currents and current loops Magnetic fields due to currents long straight wire solenoid
• 3.
  Force of B-fieldon Current + v  Force on 1 moving charge: F = q v B sin(  ) Out of the page (RHR) Force on many moving charges: F = q v B sin(  ) = (q/t) (vt) B sin(  ) = I L B sin(  ) Out of the page! B v L = vt B I = q/t + + + +
• 4.
  force is zero out of the page into the page Here  = 0 Preflight 9.1 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d. What is the direction of the force on section a-b of the wire? B I L  F = I B Lsin  a b c d B I
• 5.
  force is zero out of the page into the page Preflight 9.2 A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d. What is the direction of the force on section b-c of the wire? a b c d B I F
• 6.
  Here  = 180° Force on loop A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d. Force on section c-d is zero! Same as a-b B I L  F = I B Lsin  a b c d B I
• 7.
  force is zero out of the page into the page ACT: Force on loop (cont’d) A rectangular loop of wire is carrying current as shown. There is a uniform magnetic field parallel to the sides a-b and c-d. What is the direction of the force on section d-a of the wire? a b c d B I F
• 8.
  Net force onloop is zero . But the net torque is not ! Torque on Current Loop in B field The loop will spin in place ! Preflights 9.3, 9.4: Look from here a b c d B I F F a b c d F F B
• 9.
  Torque on CurrentLoop The loop will spin in place! Torque on loop is  = L F sin(  ) = I Lw B sin(  ) Force on sections b-c and a-d: F = I B w a b c d F F B a b c d F F B a b c d F F B Recall from Phys 101: B F F   Torque is: Lw = A ! L w
• 10.
  ACT: Torque onCurrent Loop What is the torque on the loop below?  < IAB  = IAB  > IAB x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
• 11.
  Torque on CurrentLoop It is useful to define normal vector ⊥ to loop B F F   = 180 –  Note torque will align normal parallel to B like a magnetic dipole ! Even if loop is not rectangular, as long as it is flat a b c d F F B Torque is:  normal  normal If there are N loops: a b c d F F B  normal S N
• 12.
  Current loops actlike dipoles Electron orbit and “spin” are current loops Why some materials are magnetic Nuclear Magnetic Resonance (NMR) and MRI Orbits of electrons “ spin”
• 13.
  ACT: Torque Comparethe torque on loop 1 and 2 which have identical area, and current. (1) 1)  1 >  2 2)  1 =  2 3)  1 <  2 Area points out of page for both!  = 90  = I A B sin(  B I B I (2)
• 14.
  Currents create magnetic fields Straight wire carrying current I generates a field B at a distance r: Magnitude Direction “ Right-hand rule 2”: Thumb of right hand along I Fingers of right hand along r Out-of-palm points along B “ Permeability of free space” (similar to  0 for electricity) Note: there are different versions of RHR I (out of page) B field circles wire B r
• 15.
  A long straightwire is carrying current from left to right. Near the wire is a charge q with velocity v Compare magnitude of magnetic force on q in (a) vs. (b) a) has the larger force b) has the larger force c) force is the same for (a) and (b) ACT/Preflight 9.6 q q v I v (a) r • • r (b) F F
• 16.
  Two long wirescarry opposite current What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x ACT: Adding Magnetic Fields 1) Left 2) Right 3) Up 4) Down 5) Zero
• 17.
  Force between current-carryingwires Another I towards us Currents in same direction attract! I towards us Another I away from us Currents in opposite direction repel! Example Currents in same direction Currents opposite direction I towards us B F B F
• 18.
  Comparison: Electric Field vs. Magnetic Field Electric Magnetic Source Charges Moving Charges Acts on Charges Moving Charges Force F = Eq F = q v B sin(  ) Direction Parallel E Perpendicular to v,B Field Lines Opposites Charges Attract Currents Repel +
• 19.
  What is thedirection of the force on the top wire, due to the two below? 1) Left 2) Right 3) Up 4) Down 5) Zero ACT: Force between Wires
• 20.
  B I Bis uniform everywhere inside of solenoid: n is the number of turns of wire/meter (n = N/L) B field lines look like bar magnet! Solenoid has N and S poles! Solenoids Magnitude Direction Use “Right-hand rule 2” A solenoid consists of N loops of wire B I
• 21.
  (1) Attractive(2) Zero (3) Repulsive ACT: The force between the two solenoids is …
• 22.
  Summary of Right-HandRules RHR 1 RHR 2 Alternate Force on moving q B field from current I Straight wire Solenoid I B I B I r