Solenoids

1
Solenoids

• PH 203
• Professor Lee Carkner
• Lecture 18

2
Rail Gun

• For each rail
• B m0i/2pr
• B (4pX10-7)(100000) / 2p(0.005)
• B 4 T so sum of B 8 T
• Force on conductor
• F BiL sinq
• F (8)(100000)(0.01) sin 90
• F 8000 N
• Kinetic Energy
• F ma, a F/m 8000/0.1 80000N
• v at (80000)(0.1) 8000 m/s
• KE 1/2mv2 (1/2)(0.1)(8000)2
• KE 3.2X106 J 3.2 MJ

F
X B field from each rail
i
i
3
Magnetic Field Loop

• Can apply the right hand rule all the way around
• Loop acts as a bar magnet

4
Magnetic Field Solenoid

• What happens if you stack several loops up?
• You produce a solenoid
• Field inside the solenoid is strong and uniform
  (far from the ends)

5
Solenoid Quantified

• We can write an expression for the solenoid
  magnetic field
• B m0ni
• Note that
• N is the total number of turns
• n N/L

6
Toroid

• The toroid has a radius r we can use as an
  Amperian loop
• (B)(2pr) m0iN
• B (m0iN)/(2pr)
• B is not constant and depends on where you are
  radially in the toroid

7
Magnetic Dipole

• We can parameterize the loop with a dipole
  moment, m
• m NiA
• If the loop is placed in an external magnetic
  field, it will experience a torque
• mB sin q
• where q is the angle between m and B

8
Dipole Torque

• Use the right hand rule to find the direction of
  m
• Dipoles that are not aligned with the field will
  turn until they are

9
Dipole Energy

• U -mB cos q
• When aligned with the field the energy is mB
• When opposite the field the energy is mB

10
Field from a Dipole

• A dipole is effected by external magnetic fields
  and also produces its own magnetic field
• B (m0m)/(2pz3)
• Field falls off rapidly with z

11
Next Time

• Test 2 Monday
• For Wednesday
• Read 30.1-30.4
• Problems Ch 30, P 2, 3, 4

12

• A wire is carrying a current straight towards
  you. What is the direction of the magnetic field
  of the wire?
• straight towards you
• down
• up
• circling the wire in a clockwise direction
• circling the wire in a counterclockwise direction

13

• A horizontal wire is carrying a current straight
  north. What is the direction of the magnetic
  field directly above the wire and directly below
  the wire?
• east, west
• up, down
• north, south
• up, west
• It depends on the magnitude of the current

14

• A horizontal wire is carrying a current to your
  right. What direction would a proton be
  deflected in if it traveling exactly below the
  wire also to the right?
• left
• right
• up
• down
• right at you