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

034

i ds rdB

r

������������������������������������������

02

sin

4

i dsor dB

r

0 encB ds i ����������������������������

7

0 4 10 Tmmagnetic permability A

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.

02

sin

4

i dsdB

r

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.

0 encB ds i ����������������������������

Practice with Ampere’s law

Checkpoint p.775:Which loop has the greatest

p.781: Q1, 2, 7, Prob.#1, 3, 7, 12

?B ds����������������������������

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

0 encB ds i ����������������������������

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

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:

20

32

i RB

z

(derivation on p.780)

Practice with magnetic dipoles

20

32

i RB

z

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 REarth, 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 Rsun, 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 d2B/dx2.

What spacing gives B”=0?