Download PHYS 221 Recitation

PHYS 221 Recitation
Kevin Ralphs
Week 6
Overview
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HW Questions
Electromotive Force (EMF)
Motional EMF
Farraday’s Law
Lenz’s Law
Inductance
HW Questions
Ask Away…
Electromotive Force (EMF)
• What does it tell me?
– The change in potential energy per unit charge an object
has when moved along a path
Δ𝑃𝐸
ℰ≡
𝑞
– It can also refer to the voltage measured across two
terminals
• Why do I care?
– So far we have considered conservative electric fields
which have scalar potentials
– For non-conservative fields, the change in potential energy
becomes path dependent and EMF is accounting for that
Electromotive Force (EMF)
• Why do I care?
– If a particle is free to move around in space, this is
not all that helpful, but when they are constrained
to move on a specified path (like an electronic
circuit), it becomes well-defined.
Note:
1. This is not a force, it has units of volts
2. This is not a potential, the path taken matters
very much
Motional EMF
• When a conductor moves through a magnetic
field, it acquires an EMF (this is more along
the lines of the two terminal definition)
• This happens because a Lorentz force from the
magnetic field shuffles charges to opposite
ends of the conductor
• This sets up a voltage like a parallel plate
capacitor bringing the charges into an
equilibrium
Motional EMF
Faraday’s Law
• Two earlier approximation schemes
– Electrostatics
• Stationary charges
• Conducting charges at equilibrium
𝐸 ⋅ ∆𝑙 = 0
𝐿𝑜𝑜𝑝
– Magnetostatics
• Steady Currents
Faraday’s Law
• In electrodynamics we allow non-steady currents
• This causes time varying magnetic fields bringing
Faraday’s law into effect
𝐿𝑜𝑜𝑝
∆Φ𝐵
𝐸 ⋅ ∆𝑙 = −
=Ɛ
∆𝑡
𝜕𝐵
𝛻 × 𝐸=−
𝜕𝑡
Faraday’s Law
• What does it tell me?
– A changing magnetic field creates a non-conservative
electric field
– Anything that affects that flux integral induces an EMF
in a loop
• Why should I care?
– Without this law, you could not see, there would be
no cell phones or radio: electromagnetic waves exist
because of this
– Inductors and transformers exploit this phenomenon
Lenz’s Law
• What does it tell me?
– When the flux through a loop changes, a current is
produced that fights this change
• Why should I care?
– This principle is how you determine the direction
of an induced current
Lenz’s Law
• If you are having problems with this, you are not alone
– People spend thousands of hours researching this (no
kidding)
• The idea is to find the direction of the induced
magnetic field and use the right hand rule to find the
current
• To find the direction of the induced field
– Note the direction of the original field through the loop
– Determine whether this field is getting stronger or weaker
– The direction of the induced field will maintain the status
quo
Inductance
• What does it tell me?
– The flux through a loop depends linearly on the
currents through conductors in the vicinity
(including itself)
Φ𝑀 = 𝐿𝐼 +
𝑀𝑖 𝐼𝑖
– This is a direct consequence of the principle of
superposition and magnetic fields being
proportional to the currents that create them
Inductance
• Why should I care?
– This is the sister component to the capacitor making it one
of the most fundamental electronic components
Capacitor
Inductor
Depends on geometry and
material between the plates
Depends on geometry and
material in intervening space
Proportionality between charge
and voltage
Proportionality between flux and
current
Stores energy in an electric field
Stores energy in a magnetic field
Causes current to lag voltage
Causes current to lead voltage
𝑄
𝐶
Current starts at maximum and
drops to zero
𝑑𝐼
𝑑𝑡
Current starts at zero and
increases to maximum
𝑉=
𝑉=𝐿