winter wk 6 – mon.7.feb.05 ch.29: currents cause magnetic fields –finding b field due to current...
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![Page 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](https://reader036.vdocuments.mx/reader036/viewer/2022070412/56649d7a5503460f94a5e28d/html5/thumbnails/1.jpg)
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
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B from I: direction
You know how to find the DIRECTION of a B field using the RH rule for currents:
Straight wireSolenoid
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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
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02
sin
4
i dsor dB
r
0 encB ds i ����������������������������
7
0 4 10 Tmmagnetic permability A
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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
![Page 5: 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](https://reader036.vdocuments.mx/reader036/viewer/2022070412/56649d7a5503460f94a5e28d/html5/thumbnails/5.jpg)
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 ����������������������������
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Practice with Ampere’s law
Checkpoint p.775:Which loop has the greatest
p.781: Q1, 2, 7, Prob.#1, 3, 7, 12
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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 ����������������������������
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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
![Page 9: 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](https://reader036.vdocuments.mx/reader036/viewer/2022070412/56649d7a5503460f94a5e28d/html5/thumbnails/9.jpg)
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
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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)
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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?
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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?
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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?