Учебное пособие Казань-2016 Сайфуллина М. Н., Хабирова Н. М. English for Physicists

Magnetic field of a long, straight wire

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Posobie dlya fizikov Habirova Sajfullina ispravv
ркк элтех, 1 сабак мудл Селим (1), бжб тжб 11, Лекция 8. Айнымалы ток

Amperes law
Magnetic fields of the loop, solenoid, and toroid

Magnetic field of a long, straight wire
A current
‐
carrying wire generates a magnetic field of magnitude B in circles around the wire. The
equation for the magnetic field at a distance r from the wire is
, where I is the current in the wire and μ (the Greek letter mu) is
the proportionality constant. The constant, called the permeability constant,
has the value
.
The direction of the field is given by a second right
‐
hand rule, shown in Figure 4. Using the second
right-hand rule you can determine the direction of the magnetic field resulting from a current.
Grasp the wire so that your thumb points in the direction of the current.
Your fingers will curl around the wire in the direction of the magnetic field.
Ampere's law
Ampere's law allows the calculation of magnetic fields. Consider the circular path around
the current. The path is divided into small elements of length (Δ l). Note the component of B
that is parallel to l and take the product of the two to be B
∥
l. Ampere's law states that the sum
of these products over the closed path equals the product of the current and μ ,
.
Magnetic fields of the loop, solenoid, and toroid
A current generates a magnetic field, and the field differs as the current is shaped into (a) a loop,
(b)
a solenoid (a long coil of wire), or (c) a toroid (a donut
‐
shaped coil of wire). The equations for the
magnitudes of these fields follow. The direction of the field in each case can be found by the second
right
‐
hand rule. Figure 5 illustrates the fields for these three different configurations.
71

Figure 5
Magnetic field resulting from (a) a current loop, (b) a solenoid, and (c) a toroid.
a)
The field at the center of a single loop is given by
, where r
is the radius of the loop.
b)
The field due to a solenoid is given by B = μ
0
NI, where N is the
number of turns per unit length.
c)
The field due to a toroid is given by
, where R is the radius
to the center of the toroid.
(Adopted from
www.cliffsnotes.com
)

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