Transcript Ch. 28 Sources of Magnetic Fields / Ampere's Law

Source of Magnetic Field Ch. 28
B field of current element
Law of Biot and Savart
B field of current-carrying wire
Force between conductors
B field of circular current loop
Ampere’s Law
Applications of Ampere’s Law
C 2012 J. F. Becker
(sec. 28.2)
(sec. 28.3)
(sec. 28.4)
(sec. 28.5)
(sec. 28.6)
(sec. 28.7)
Learning Goals - we will learn: ch 28
• How to calculate the magnetic field
produced by a long straight currentcarrying wire, using Law of Biot & Savart.
• How to calculate the magnetic field
produced by a circular current-carrying
loop of wire, using Law of Biot & Savart.
• How to use Ampere’s Law to calculate the
magnetic field caused by symmetric
current distributions.
(a) Magnetic field caused by the current element Idl.
(b) In figure (b) the current is moving into the screen.
Magnetic field around a long, straight conductor. The
field lines are circles, with directions determined by
the right-hand rule.
xo
Magnetic field
produced by a
straight currentcarrying wire of
length 2a. The
direction of B at
point P is into the
screen.
Law of Biot and Savart
dB = mo / 4p (I dL x r) /
3
r
Use Law of Biot and Savart, the integral is simple!
dB = mo / 4p (I dL x r) /
3
r
Magnetic field caused by a circular loop of current. The
current in the segment dL causes the field dB, which
lies in the xy plane.
xo
Magnetic field
produced by a
straight currentcarrying wire of
length 2a. The
direction of B at
point P is into the
screen.
Law of Biot and Savart
dB = mo / 4p (I dL x r) /
3
r
Parallel conductors carrying currents in the same
direction attract each other. The force on the upper
conductor is exerted by the magnetic field caused by
the current in the lower conductor.
Ampere’s Law
Ampere’s Law states that the integral of B around
any closed path equals mo times the current, Iencircled,
encircled by the closed loop.
Eqn 28.20
We will use this law to obtain some useful results by
choosing a simple path along which the magnitude of B is
constant, (or independent of dl). That way, after taking
the dot product, we can factor out |B| from under the
integral sign and the integral will be very easy to do.
See the list of important results in the
Summary of Ch. 28 on p. 983
Some (Ampere’s Law) integration paths for the line
integral of B in the vicinity of a long straight conductor.
Path in (c) is not useful because it does not encircle the
current-carrying conductor.
To find the magnetic field at radius r < R, we apply
Ampere’s Law to the circle (path) enclosing the red
area. For r > R, the circle (path) encloses
the entire conductor.
B = mo n I, where n = N / L
A section of a long, tightly wound solenoid centered on
the x-axis, showing the magnetic field lines in the
interior of the solenoid and the current.
COAXIAL CABLE
A solid conductor with radius a is insulated from a
conducting rod with inner radius b and outer radius c.
Review
See
www.physics.sjsu.edu/becker/physics51
C 2012 J. F. Becker