Biot-Savart Law Amp

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Biot-Savart LawAmpères Law

• Fields and forces for current in straight wires
• Ampères Law

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Example 1 Long parallel wires
L
a
b
I1
d
I2
Find force on current I1 in segment ab due to
current I2 (magnitude direction)
(Take I1 20A, I230A, d0.01m, L1.5m)
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Solution
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I2
Quiz
The two long wires shown cross at right angles.
The horizontal wire 1 is fixed.How will the red
wire move when the currents are turned on?
I1
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Ampères Law (an integral theorem)
For any closed path
The current flows through the surface bordered by
the path.
Positive current is out of the page through the
shaded surface (right hand rule)
direction of integration determines positive
current direction
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Calculating B from Amperes Law
For a few simple shapes, we can calculate the
field B easily from Amperes Law. The steps

1. use symmetry to choose an appropriate path
2. determine the direction of B from RHR.
3. calculate (in terms of B)
4. calculate Iencircled
5. apply Amperes Law to get B

Amperes Law holds only for steady currents
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Quiz Long Straight Wire
On which of the curves C1, C2, and C3 is
C 2
B
I

• i) smallest
• largest
• zero

C 1
C 3
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Example 2 Long Straight Wire
Show that the field produced by a current I in a
long straight wire at distance r from the wire
is
Steps
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Solution
I
B
ds
field line
path of integration
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Example 3
Wire, radius R, uniform current density
R
x x x x x x x x x x x x x x x x x x x x x x x x
x x x x
J
r
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Solution
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Example 4
What is the magnetic field inside and outside A
hollow copper pipe carrying current I?
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Example 5
What is the magnetic field inside and outside A
coaxial cable carrying equal currents (in
opposite directions) on the inner and outer
conductors?
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Solution
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Infinitely Long Solenoid (long straight
coil/helix)
Current I flows in each turn of the coil. The
number of turns of wire per meter of solenoid is
called the turn density n.
I
B inside the solenoid is uniform and has magnitude
and is uniform.What is the direction of B?
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Field patterns for circular coils
Single Coil
B
I
Several Coils