Lecture 14 Magnetic Domains Induced EMF Faraday’s Law Induction Motional EMF.
Transcript of Lecture 14 Magnetic Domains Induced EMF Faraday’s Law Induction Motional EMF.
Lecture 14
Magnetic Domains Induced EMF Faraday’s Law Induction Motional EMF
Magnetic Field of a Current Loop – Equation The magnitude of the magnetic field
at the center of a circular loop with a radius R and carrying current I is
With N loops in the coil, this becomes2
oIBR
2oIB NR
Magnetic Field of a Solenoid
If a long straight wire is bent into a coil of several closely spaced loops, the resulting device is called a solenoid
It is also known as an electromagnet since it acts like a magnet only when it carries a current
Magnetic Field of a Solenoid, 2 The field lines inside the solenoid
are nearly parallel, uniformly spaced, and close together This indicates that the field inside the
solenoid is nearly uniform and strong The exterior field is nonuniform,
much weaker, and in the opposite direction to the field inside the solenoid
Magnetic Field in a Solenoid, 3 The field lines of the solenoid resemble
those of a bar magnet
Magnetic Field in a Solenoid, Magnitude The magnitude of the field inside a
solenoid is constant at all points far from its ends
B = µo n I n is the number of turns per unit length n = N / ℓ
The same result can be obtained by applying Ampère’s Law to the solenoid
Magnetic Field in a Solenoid from Ampère’s Law A cross-sectional
view of a tightly wound solenoid
If the solenoid is long compared to its radius, we assume the field inside is uniform and outside is zero
Apply Ampère’s Law to the blue dashed rectangle
Fig. 19-34, p.648
Fig. Q19-7, p.650
Magnetic Effects of Electrons – Orbits An individual atom should act like a magnet
because of the motion of the electrons about the nucleus Each electron circles the atom once in about
every 10-16 seconds This would produce a current of 1.6 mA and a
magnetic field of about 20 T at the center of the circular path
However, the magnetic field produced by one electron in an atom is often canceled by an oppositely revolving electron in the same atom
Magnetic Effects of Electrons – Orbits, cont The net result is that the magnetic
effect produced by electrons orbiting the nucleus is either zero or very small for most materials
Magnetic Effects of Electrons – Spins Electrons also
have spin The classical
model is to consider the electrons to spin like tops
It is actually a quantum effect
Magnetic Effects of Electrons – Spins, cont The field due to the spinning is
generally stronger than the field due to the orbital motion
Electrons usually pair up with their spins opposite each other, so their fields cancel each other That is why most materials are not
naturally magnetic
Magnetic Effects of Electrons – Domains In some materials, the spins do not
naturally cancel Such materials are called ferromagnetic
Large groups of atoms in which the spins are aligned are called domains
When an external field is applied, the domains that are aligned with the field tend to grow at the expense of the others This causes the material to become
magnetized
Domains, cont Random alignment, a, shows an
unmagnetized material When an external field is applied, the
domains aligned with B grow, b
Domains and Permanent Magnets In hard magnetic materials, the domains
remain aligned after the external field is removed The result is a permanent magnet
In soft magnetic materials, once the external field is removed, thermal agitation causes the materials to quickly return to an unmagnetized state
With a core in a loop, the magnetic field is enhanced since the domains in the core material align, increasing the magnetic field
Fig. 19-37, p.649
Fig. 19-37a, p.649
Fig. 19-37b, p.649
Fig. 19-37c, p.649
Michael Faraday 1791 – 1867 Great experimental
scientist Invented electric
motor, generator and transformers
Discovered electromagnetic induction
Discovered laws of electrolysis
p.661
Faraday’s Experiment – Set Up A current can be produced by a
changing magnetic field First shown in an experiment by Michael
Faraday A primary coil is connected to a battery A secondary coil is connected to an ammeter
Faraday’s Experiment The purpose of the secondary circuit is to
detect current that might be produced by the magnetic field
When the switch is closed, the ammeter reads a current and then returns to zero
When the switch is opened, the ammeter reads a current in the opposite direction and then returns to zero
When there is a steady current in the primary circuit, the ammeter reads zero
Faraday’s Conclusions An electrical current is produced by a
changing magnetic field The secondary circuit acts as if a source
of emf were connected to it for a short time
It is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic field
Magnetic Flux The emf is actually induced by a change
in the quantity called the magnetic flux rather than simply by a change in the magnetic field
Magnetic flux is defined in a manner similar to that of electrical flux
Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop
Magnetic Flux, 2 You are given a loop
of wire The wire is in a
uniform magnetic field
The loop has an area A
The flux is defined as ΦB = BA = B A cos θ
θ is the angle between B and the normal to the plane
B
Magnetic Flux, 3
When the field is perpendicular to the plane of the loop, as in a, θ = 0 and ΦB = ΦB, max = BA
When the field is parallel to the plane of the loop, as in b, θ = 90° and ΦB = 0
The flux can be negative, for example if θ = 180° SI units of flux are T. m² = Wb (Weber) Demo
Magnetic Flux, final The flux can be visualized with respect to
magnetic field lines The value of the magnetic flux is
proportional to the total number of lines passing through the loop
When the area is perpendicular to the lines, the maximum number of lines pass through the area and the flux is a maximum
When the area is parallel to the lines, no lines pass through the area and the flux is 0
Electromagnetic Induction –An Experiment
When a magnet moves toward a loop of wire, the ammeter shows the presence of a current (a)
When the magnet is held stationary, there is no current (b)
When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c)
If the loop is moved instead of the magnet, a current is also detected Demo
Electromagnetic Induction – Results of the Experiment A current is set up in the circuit as
long as there is relative motion between the magnet and the loop The same experimental results are
found whether the loop moves or the magnet moves
The current is called an induced current because is it produced by an induced emf
Faraday’s Law and Electromagnetic Induction The instantaneous emf induced in a
circuit equals the time rate of change of magnetic flux through the circuit
If a circuit contains N tightly wound loops and the flux changes by ΔΦB during a time interval Δt, the average emf induced is given by Faraday’s Law:
tN B
Faraday’s Law and Lenz’ Law The change in the flux, ΔΦB, can be
produced by a change in B, A or θ Since ΦB = B A cos θ
The negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law
The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit