Winter wk 6 Mon.7.Feb.05

1
Winter wk 6 Mon.7.Feb.05

• Ch.29 Currents cause magnetic fields
• Finding B field due to current I
• How strong are B fields produced by brains?
• Force between two parallel currents
• Solenoids and dipoles
• Applications to Sun and Earth

Energy Systems, EJZ
2
B from I direction

• You know how to find the DIRECTION of a B field
  using the RH rule for currents
• Straight wire Solenoid

3
B from I magnitude

• B is perpendicular to I, and weaker with
  distance
• In general, Biot-Savart law
• Easier Amperes law

4
Ex Brain currents

• Use Biot-Savart law to estimate the magnetic
  field at your skull (r 2 cm away) due to a
  neuron current of i10 mA over a distance of
  ds1mm.

5
B due to long, straight current

• See complicated derivation from Biot-Savart law
  on p.767.
• Easier with Amperes law
• Notice the conceptual similarity to Gauss Law.

6
Practice with Amperes law

• Checkpoint p.775
• Which loop has the greatest
• p.781 Q1, 2, 7, Prob.1, 3, 7, 12

7
Magnetic field of a solenoid

• Use Amperes law to evaluate B
• inside the solenoid. (Recall your
• observations about the B outside,
• and let n turns/length.)
• Practice 40

8
Force between currents

• Last week we found the DIRECTION of the force on
  I2 due to the field B1 of I1
• I1
• I2
• The MAGNITUDE of the force is F/L I2xB1

9
Practice with force between currents

• Checkpoint p.772 Which wire experiences the
  greatest force, due to the currents in the other
  two wires?
• Which wire experiences the smallest force?
• p.781 Q4

10
Current loop as a magnetic dipole

• The magnetic field on the z-axis increases with
  current (and with loop size R),
• and decreases with distance

(derivation on p.780)
11
Practice with magnetic dipoles
Which set of loops has the greatest B field at
the central dot? Which has the smallest B
field?
12
Applications to Sun and Earth

• How strong is the Earths magnetic field 100 km
  above a pole (near where aurorae occur)?
• If the Earths surface field at the pole is about
  1 Gauss, and if this field were produced by a
  simple dipole current at about 0.6 REarth, how
  strong would that current have to be?
• If the Suns surface field at a pole is about 10
  Tesla, and the field were produced by a simple
  dipole current at about 0.7 Rsun, how strong
  would that current have to be?

13
Helmholtz coils

• Optional 80 p.789 These coaxial coils produce
  a relatively uniform B field in the center if
  their spacing is right, good for q/m experiment.
• What is the field at the center?
• Find dB/dx.
• Why is B0 at center?
• (b) Find d2B/dx2.
• What spacing gives B0?