Download Chris Khan 2008 Physics Chapter 23 Changing magnetic fields can

Chris Khan 2008
Physics Chapter 23
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Changing magnetic fields can create electric fields, causing static charges to move. A changing magnetic field
can produce an electric current like a battery.
When a current appears without direct contact with another circuit, this is referred to as an induced current.
This induced current behaves the same way as a current produced by a battery with an emf and therefore, the
changing magnetic field creates an induced emf.
o The magnitudes of the induced current and induced emf are proportional to the rate of change of the
magnetic field – the more rapidly the magnetic field changes, the greater the induced emf.
Magnetic flux is a measure of the number of field lines that cross a given area.
o When B is perpendicular to the surface, φ becomes BA. When B is parallel, φ = 0. The SI unit of
measure is the T•m2 or the Wb (weber).
o Consider a circular loop with radius 2.5 cm and B of 0.625 T. What is the magnetix flux when the
angle with B is 0, 30, 60 or 90 degrees? Answer below is for 0 degrees. Do the same for the rest.
To find the induced emf, Faraday used the following equation:
where N represents the number of
loops in a coil.
o A bar magnet is moved rapidly towards a 40-turn circular coil of wire. As the magnet moves, the
average value of Bcosθ over the area increases from 0.0125 T to 0.450 T in 0.250 s. If the radius is
3.05 cm and the resistance is 3.55 Ω, what is the magnitude of the induced emf and induced current?
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Lenz’s Law tells us that an induced current always flows in a direction that opposed the change that caused it.
For example, pushing a magnet towards a conducting ring makes them repel, but bringing the magnet away
from the ring makes the ring attracted to the magnet.
When dropping a rod in the vertical direction across wires in such a way that the rod completes the loop, flux
decreases as area decreases, so in order to make up for this, magnetic field must be increased. To do this, use
Lenz’s Law. The change is that the rod is falling downwards due to gravity, so the force must be pointing
upwards. Using the right hand rule, since the magnetic field is going into the page, the current must be going
from right to left. Eventually, this increasing magnetic force opposes gravity to the point where acceleration
vanishes.
o If a metal ring is falling from a region with magnetic fields pointing out of the page into a region with
no magnetic fields, what direction is the induced current pointing in? Since we need to make more
magnetic field lines coming out of the page, the induced current must be moving counterclockwise.
Considering motional emf, the emf produced by motion, the setup consists like the example above the previous
one: a rod slides on a U-shaped wire to complete the loop. If you are moving the rod with constant speed, it
moves a distance of v∆t in the time ∆t, so the area increases by ∆A = (v∆t)l. The increase in magnetic flux is
∆Φ = B∆A = Bvl∆t. Also, we know
Also, since
. From this, E = Bv.
. To keep the rod moving with a constant speed v, note that it carries a current of
magnitude I = Bvl/R at right angles to B.
is:
by multiplying this force by velocity.
Since the length is l, the
magnetic force
The mechanical power delivered by the external force can be found
o
There is a light bulb in a circuit with a resistance of 12 Ω that consumes 5 W of power. The rod is 1.25
m along and moves to the left with a constant speed of 3.1 m/s. What is B and the force to maintain v?
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The expression for the emf of a rotating coil is:
o The coil in a generator has 100 turns and an area of 2.5 x 10 -3 m2. It is desired that the maximum emf
of the coil be 120 V when it rotates at 60 cycles per second. What is the B required for this generator?
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Induced emf can be written as:
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The inductance of a solenoid is given as:
o
where the SI unit is the henry. Also,
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A 500-turn solenoid is 8 cm long. When the current is decreased from 0 to 2.5 A in 0.35 s the
magnitude of the ind. emf is 0.012 V. Find the inductance and the cross-sectional area of the solenoid.
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The amount of energy stored in an inductor is given as:
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The transformer equation is given as:
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