Download Magnetism

Physics 272
February 24
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
[email protected]
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Kirchhoff's rules
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Kirchhoff's junction rule:
Algebraic sum of currents is zero at any junction.
Conservation of charge
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Algebraic sum of potential differences is zero in any
loop.
Electrostatic force is conservative. Path does not
matter → potential energy is the same after going around
a loop
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Charging a battery
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Ammeter
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Measure current that path through the meter
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Good Ammeter has a small internal resistance
pointer moves because of
magnetic field interactions
with electric current
circuit
element
full scale
current
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Voltmeters
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Voltmeters should have a large resistance such that
connecting them in parallel is not altering the
current of the circuit
Ammeter and Voltmeter in combination can
measure resistance and power
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R-C circuits
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So far: constant emfs and constant current
Next steps: time dependent potentials, currents, and
powers
What happens when you charge a capacitor?
many devices use charging and discharging
constantly:
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Flashing traffic lights
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Car turn signals
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Flash units
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Charging a capacitor
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Ideal battery (zero internal resistance)
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Capacitor initially uncharged
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Close switch → charge capacitor
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Assume:
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current starts at the
same time everywhere
in the circuit
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Current is the same
everywhere for a particular
moment in time
Lower case quantities are time dependent quantities
in the following calculations
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Charging a capacitor
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Capacitor charges:
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vbc increases (charge builds up)
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vab decreases (Kirchhoff's loop rule)
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Current decreases (Ohm's law)
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Charging a capacitor
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Eventually:
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Capacitor fully charged
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Current stops flowing
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Charging a capacitor
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Charge at any time t during the charging process:
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Charging a capacitor
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Current and time constant
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time constant: =RC
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 small: capacitor charges quickly
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 large: capacitor charges slowly
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Charge and current processes happen on the same
time scale 
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Charging a capacitor
Charge build-up
Current drop
q/Qf
i/I0
t
t
i/I0
Slope is -1/(RC)
→ measure properties
Logarithmic plot
t
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Power approach
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Energy conservation:
-Ri2
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Half of the energy is stored in capacitor
Other half is dissipated in resistor (does not depend on C, R, )
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Discharging a capacitor
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Remove battery
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Time constant RC stays the same
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Charge goes exponentially to zero
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Example
For a charging capacitor, the ratio of charge to final charge on the
capacitor and the ratio of current to the initial current add up to 1.
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Power distribution systems
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Appliances at home are always operated in parallel
to the power source
Modern houses have two lines with opposite polarity
coming in (hot lines)
A third line is grounded and provides the neutral
potential
Maximum current is limited by resistance of the
wires (RI2 power loss)
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12 gauge wire (2.05mm → safe for 20A without
overheating)
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Thicker wires for, e.g.,main power lines, dryers
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Circuit overloads and short circuits
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Overload/overheat protection is provided by fuses
Fuses are designed to break circuits depending on the
maximum load allowed on the wires
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Installed on hot side of incoming line
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Fuse examples:
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lead-tin alloy with low melting temperature
→ melts when too hot
→ breaks circuit (one-time use)
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Electromagnet or bimetallic strip interrupts circuit (can be reset)
Short circuit: neutral and hot side are in contact
→ large current can melt wires!
3 prong connectors connect, e.g., metal housing to
ground line and can prevent shocks
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Where we stand
Electric charges are
sources of electric fields
0 (constant time, conservative
electric force)
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Measuring magnetic fields with test charges
http://www.youtube.com/watch?v=YbzBTdU7iRU
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Measure deflection of moving charges in the presence of a magnetic
field
Example:
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old televisions contained an electron beam in a cathode-ray tube
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Velocity is known
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If beam and magnetic field (anti)parallel → no force → no deflection
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If beam and magnetic perpendicular → maximum deflection
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Magnetism
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Examples: permanent
magnets, compass in
earth electric field
Magnetic forces arise
from moving electric
charges
Electric charges react to
magnetic field
Source: http://de.wikipedia.org/wiki/Magnet
First: focus on how electric charges react to magnetic
fields
Permanent magnets:
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Exert forces on each other
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Exert forces on unmagnetized objects containing iron
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Magnetic poles vs. electric charge
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Initially: magnets described in terms of poles
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North: bar shaped magnetic material (free to rotate) points
North
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South: bar shaped magnetic material (free to rotate)
points South
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North and South attract each other
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North-North and South-South repels each other
Objects containing iron are attracted by South and
North poles
Earth is a magnet:
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geographic poles close to magnetic poles: not totally
parallel
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Magnetic axis moves
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Magnetic poles vs. electric charge
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Important: no isolated magnetic North and
South poles exist
Major difference to positive and negative
electric charges
Ørsted found that a compass needle
was deflected by a current carrying
wire
Hans Christian Ørsted
1777-1851
Magnetic forces are due to
interactions of moving electrons in atoms
Source: http://de.wikipedia.org/wiki/Hans_Christian_%C3%98rsted
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Magnetized objects have coordinated motion of certain
atomic electrons
Unmagnetized objects do not have such a coordinated
motion
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Magnetic field
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A moving charge or a current creates a magnetic
field in the surrounding space (in addition to electric
field)
The magnetic field exerts a force on any other
moving charge or current that is present in the field.
For now: don't worry about how exactly magnetic
field is created.
Magnetic field is a vector field: a vector associated
with each point in space.
Direction towards the north pole of a compass
needle.
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Magnetic forces on moving charges
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Magnitude of the force is proportional to amount of
charge
Magnitude of the force is proportional to the
magnetic field strength.
Magnitude of the force is proportional to the velocity
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electric force is always the same: no matter if charge
moves or not!
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Particle at rest does not feel magnetic force
Force is perpendicular to the velocity and magnetic
field
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Magnetic forces on moving charges
Right hand rule
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Charges of same amount, but
opposite sign
→ feel force of same magnitude,
but opposite direction
Force (direction
of deflection)
magnetic
field B
velocity v
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Magnetic forces on moving charges
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Magnetic field of the earth: 0.1mT
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Magnetic field in atoms: 10T
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Largest magnetic field in lab: 45T
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Pulse magnetic fields produce up to: 120T
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Magnetic field and electric field:
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The World's Strongest Magnet
http://www.youtube.com/watch?v=6wH1kq7gfuU
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Additional material
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A complex network
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Magnetism
http://www.youtube.com/watch?v=jq8WOUFeCcg
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