Physics 014 Induction

Faraday’s Law Experiment #1

Faraday’s Law Experiment #2

Faraday’s Law Current produced in loop is called the induced current The work done per charge to produce the current is called the induced emf The process of producing the current and emf is called induction

Faraday’s Law An emf is induced in the loops when the number of magnetic field lines that pass through the loop is changing

Faraday’s Law First, define the magnetic flux through a loop as

Faraday’s Law The emf induced in a conducting loop is equal to the rate at which the magnetic flux through that loop changes with time.

Faraday’s Law We may write Faraday’s law as

Faraday’s Law For a coil of N turns

??? The graph shows B(t) of a uniform magnetic field throughout a conducting loop with the direction perpendicular to the plane of the loop. Rank the regions of the graph according to the magnitude of the induced emf.

Faraday’s Law Lenz’s law: An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current

Faraday’s Law Field due to current opposes flux change

??? For three situations in which identical circular conducting loops are in uniform magnetic fields that are increasing or decreasing in magnitude at identical rates. Rank the situations according to the magnitude of the induced current in the loops

Faraday’s Law

Faraday’s Law From the above reasoning we conclude that: A changing magnetic field produces an electric field

Faraday’s Law We may now rewrite Faraday’s law as,

??? For the regions, a uniform magnetic field extends directly out of or into the page, with the direction indicated only for a. The field is increasing in magnitude the same in all regions (same areas too). Determine the direction of the field in all regions.

Inductors and Inductance An inductor is typically a type of solenoid

Inductors and Inductance For an inductor with N turns, a current i producing a flux ΦB The inductance is

Inductors and Inductance The SI unit of inductance is the henry 1 henry = 1 H = 1 T m2/A

Inductors and Inductance Applying Faraday’s law to an inductor: An induced emf appears in any coil in which the current is changing

Inductors and Inductance Combining the definition of inductance and Faraday’s law

Inductors and Inductance

Energy in a magnetic field Just as a capacitor stored energy in an electric field, an inductor stores energy in a magnetic field

??? For the induced emf in the coil, which describes the current through the coil: (a) constant and rightward, (b) constant and leftward, (c) increasing and rightward, (d) decreasing and rightward, (e) increasing and leftward, (f) decreasing and leftward ?

RL circuits Let’s now examine RL circuits,

RL circuits For the switch connected to a in the diagram we find (rise of current) where

RL circuits For the case when the b terminal is connected (decaying current)

??? For the circuits with three identical batteries, inductors and resistors, rank the circuits according to the current through the battery (a) just after the switch is closed and (b) a long time later.