Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Lecture 17

Chapter 33

Faraday’s Law

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Physics II

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Electromagnetic inductionWe saw that a magnetic field could be produced with an electric current. The question arose as to whether electric current could be produced from a magnetic field.

El. current Magn. field

El. current Magn. field

This discovery changed the world.

It allowed making electricity to power industries.

curious

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Electromagnetic inductionBy experimenting Faraday concluded that a changing magnetic field can produce an electric current, which is called an induced current.

The process is called electromagnetic induction.

I

" " I

When a bar magnet is pushed into a coil of wire, it causes a momentary deflection of the current‐meter needle.Holding the magnet inside the coil has no effect.A quick withdrawal of the magnet deflects the needle in the other direction.

A changing “something”(magnetic field?) induces an EMF

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Magnetic Flux

To write an expression for an EMF, we need to introduce the magnetic flux(it is very similar to the electric flux)

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

The Area Vector (recall)

Let’s define an area vector to be a vector in the direction of, perpendicular to the surface, with a magnitude A equal to the area of the surface.

Slide 33-44

Vector has units of m2.

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Magnetic Flux

The magnetic flux measures the amount of magnetic field passing through a loop of area A if the loop is tilted at an angle from the field:

θ

The SI unit of magnetic flux is the weber:1 weber = 1 Wb = 1 T m2

In the case when magnetic field is not uniform and a surface is not flat, than the magnetic flux is

⋅

B=constA=const

Theta=const,So the flux is const

ConcepTest Magnetic Flux

A) yesB) no

The metal loop is being pulled through a uniform magnetic field. Is the magnetic flux through the loop changing?

B=constA=const

Theta=changes,So the flux is NOT const

ConcepTest Magnetic Flux II

A) yesB) no

The metal loop is rotating in a uniform magnetic field. Is the magnetic flux through the loop changing?

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Faraday’s Law

Now, after introducing the magnetic flux, we can write the Faraday’s Law

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Faraday’s Law

Faraday’s law of induction: the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit:

Now with the definition of flux, we can write mathematically what Faraday saw experimentally

)So we can induce EMF by changing:

Spinning a loop

θa loop is shrunk

B, θ, A:

(It turns out that “something” is the magnetic flux)

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Lenz’s Law

To avoid dealing with this minus, we will calculate EMF in two steps:

The minus sign gives the direction of the induced emf.

1)

2) Apply Lenz’s Law

i.e. “Any system doesn’t like changes”It opposes to a growing flux

AndSupports a dying flux

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Lenz’s Law (example)

has CW direction

Pushing the bar magnet into the loop causes the magnetic flux to increase in the upward direction.

To oppose the change in flux, which is what Lenz’s law requires, the loop itself needs to generate an downward-pointing magnetic field.

The induced current ceases as soon as the magnet stops moving.

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Example (Lenz’s Law)

I

The current in the straight wire is decreasing.

has CW direction

ConcepTest Lenz’s lawA) There is a clockwise induced current

in the loop.

B) There is a counterclockwise inducedcurrent in the loop 

C) There is no induced current in the loop.

The current in the straight wire is increasing. Which is true?

1. The wire’s B field is into the screen and increasing.

2. To oppose the increase in flux, the field of the induced current must point out of the screen.

3. From the right-hand rule, an inward field needs a ccw current.

has CCW direction

The magnetic flux through the loop

is not changing as it moves parallel

to the wire. Therefore, there is no

induced current.

I

1) clockwise

2) counterclockwise

3) no induced current

What is the induced current if

the wire loop moves in the

direction of the yellow arrow?

ConcepTest Loop and Wire II

= const

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Faraday’s Law for a U-shaped rail/rod systemLet’s apply Faraday’s law for a conducting rod sliding on a U-shaped conducting rail. B is perpendicular to the plane of the rail.

The EMF induced in the loop is:

The induced current flows through the loop:

We can find the induced emf and current by using Faraday’s law and Ohm’s law:

has CCW direction

Direction of the induced current:

ConcepTest Faraday’s LawA) 200 VB) 20 VC) 2 VD) 0.5 VE) 0.2 V

The induced emf around this loop is

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

What you should readChapter 33 (Knight)

Sections 33.3 33.4 33.5

Department of Physics and Applied Physics DanylovPHYS.1440 Lecture 17

Thank youSee you on Tuesday