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

B from I: direction You know how to find the DIRECTION of a B field using the RH rule for currents: Straight wireSolenoid

B from I: magnitude B is perpendicular to I, and weaker with distance: In general, Biot-Savart law: Easier: Ampere’s law

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 i=10  A over a distance of ds=1mm.

B due to long, straight current See complicated derivation from Biot-Savart law on p.767. Easier with Ampere’s law: Notice the conceptual similarity to Gauss’ Law.

Practice with Ampere’s law Checkpoint p.775: Which loop has the greatest p.781: Q1, 2, 7, Prob.#1, 3, 7, 12

Magnetic field of a solenoid Use Ampere’s law to evaluate B inside the solenoid. (Recall your observations about the B outside, and let n = turns/length.) Practice: #40

Force between currents Last week we found the DIRECTION of the force on I 2 due to the field B 1 of I 1 : I 1 I 2 The MAGNITUDE of the force is F/L = I 2 xB 1

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

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)

Practice with magnetic dipoles Which set of loops has the greatest B field at the central dot? Which has the smallest B field?

Applications to Sun and Earth How strong is the Earth’s magnetic field 100 km above a pole (near where aurorae occur)? If the Earth’s surface field at the pole is about 1 Gauss, and if this field were produced by a simple dipole current at about 0.6 R Earth, how strong would that current have to be? If the Sun’s surface field at a pole is about 10 Tesla, and the field were produced by a simple dipole current at about 0.7 R sun, how strong would that current have to be?

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 B’=0 at center? (b) Find d 2 B/dx 2. What spacing gives B”=0?