PHYS 221 Recitation

Kevin RalphsWeek 6

Overview

• 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

– 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 volts2. 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

– 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

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)

– 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 componentsCapacitor 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

Current starts at maximum and drops to zero

Current starts at zero and increases to maximum