19'4 Magnetic field due to a current

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19.4 Magnetic field due to a current

• Magnetic field due to current
• Amperes Law
• Force between current carrying wires

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Where do magnetic fields come from?
Hans Oersted 1820
Current off
Current on I
Magnetic fields due to electric current
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Magnetic field lines around a current in straight
wire -circle with radius R
Direction of B given by right hand rule
Thumb-along I Fingers- around I point along B
permeability of free space 4px10-7Tm/A
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Amperes Law Andre Marie Ampere (1775-1836)
General relation between current and magnetic
field
closed path
I
?L - line segment B - magnetic field Bll
component of B parallel to ?L
?L
Bll
B
sum over all segments in the closed loop
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The magnetic field around a straight wire
calculated from Amperes Law
From symmetry, the B field should have a constant
value at a constant radius R.
Therefore, from Amperes Law
from Amperes Law
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A 5A current passes through a wire downward in
the vertical direction. a) At what distance R
from the wire will the magnetic field equal the
earths field B0.5x10-4 T. How will the compass
needles be deflected?
Bearth
R
I into the page
view from above
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A 5A current passes through a wire downward in
the vertical direction. a) At what distance R
from the wire will the magnetic field equal the
earths field B0.5x10-4 T. How will the compass
needles be deflected?
Bearth
R
?
BBearth
I into the page
view from above
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A power line carries a current of 100 A from east
to west. a) Find the magnitude of the B field at
a position 20 m below the line due to the
current. b) Find the direction of B.
I
B
a)
this is much smaller than the earths magnetic
field 0.5x10-4 T
South- by the right-hand rule.
b)
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Force between two current carrying wires of
length L, parallel at distance R.
B12
I1
F
R
I2
L
I1 produces a field B12 at the position of wire
2.
I2 experiences a force due to B12
Directions B inward F attractive
The force between the two wires is
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Current in same direction-
Force - Attractive
B12
I1
F
R
I2
Force - Repulsive
Current in opposite directions
B12
I1
F
R
I2
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64. Two long parallel wires with mass/length s
40g/m are supported in a horizontal plane by 6.0
cm long strings. Each wire carries current I
causing the wires to repel each other by an angle
?16o. Find I.
?16o
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Definition of current and charge based on
Amperes law
Current The ampere defined as the current
required to produce the force between current
carrying wires separated by distance R.