Amp

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Ampères Law (??????)
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Illustration of Ampères law
See the right figure, a infinitely long
current carrying wire with a current I. We choose
a loop as shown in the figure and calculate the
curve integral of the magnetic field
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Generalization (????)
As shown in the figure below, loop C1 circles
an infinitely long current-carrying wire, and C2
circles no current, one integrate the magnetic
field along the loops as following
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The curl of a magnetic field is current density
vector. (??????,????????????)
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Vector Potential (???)
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Applications of Ampères law
Ampères law is valid only for steady current.
In the electrostatic field, we apply Gausss law
to evaluate the electric field due to symmetric
charge distributions we will now apply the
Ampères law to evaluate the magnetic field of
the systems of symmetry.
It is important to choose a proper Gaussian
surface in using Gausss law to evaluate the
electric field. Similarly, it is important to
choose a proper loop in applying the Ampères law
to evaluate the magnetic field.
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The magnetic field created by a long straight
current-carrying wire
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Magnetic field of a long, straight
current-carrying solenoid
Weve calculated the magnetic field of points
on the axis of a solenoid starting from
Biot-Savart law and discuss the two special
cases the infinite long and semi-infinite
long solenoid, the results are presented in the
following.
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When a solenoids turns are closed spaced
and its length is large compared with its radius,
it approaches the case of an ideal solenoid, the
field outside of the solenoid is zero, and the
field inside is uniform. We will use ideal
solenoid as a simplification model for a real
solenoid.
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The Magnetic Field Created by a Toroid
A device called a toroid is often used to
create an almost uniform magnetic field in some
enclosed area. The device consists of a
conducting wire wrapped around a ring (a torus)
made of a non-conducting material. For a toroid
having N closely spaced turns of wire and air in
the torus, calculate the magnetic field in the
region occupied by the torus, a distance r from
the centre.
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Therefore, magnetic field inside a toroid
varies as 1/r and hence is non-uniform. If r is
large compared with the cross sectional radius of
the torus, however, the field is almost uniform
inside the toroid. For an ideal toroid, in which
the turns are closed spaced, the magnitude of the
magnetic field external to the toroid is zero. In
reality, the turns of a toroid form a helix
rather than circular loops. As a result a
small field always exists external to the coin.

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Magnetic Field of An Infinite Current-carrying
Plane
(Eg. 26-5) The current density flowing through
an infinite current-carrying plane is . Find the
magnetic field in space.
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Fundamentals of Magnetostatics
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The End