L16 Ch33 Su15 - University of Massachusetts Lowell

Department of Physics and Applied Physics95.144, Summer 2015, Lecture 16

Lecture 16

Chapter 33

Faraday’s Law

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

Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

07.28.2015Physics II


Motional EMFConsider a conductor of length l that moves with velocity v through a perpendicular magnetic field B.

B


Motional EMF

Let’s calculate the potential difference between ends:

∙ ∙

It is called the motional EMF

(downward, -y direction)


Example:A plane flies in the Earth’s magnetic field (B = 5x10-5T) with v=1000 km/h; l=70m (between the wings)

(not very significant to consider)

ConcepTest 3 Motional EMF 2

A metal bar moves through a magnetic field. The induced charges on the bar are:

So the magnetic force qvB on a positive charge is to the left, so positive charge will be accumulated near the left side of the bar,

ConcepTest 2 Motional EMF 1

A metal bar moves through a magnetic field. The induced charges on the bar are:

∥So the magnetic force is zero and there is no charge separation, no motional EMF


Induced current in a circuit (rod moving to the right)

Consider a conducting rod sliding on a U-shaped conducting rail. So here we completed a circuit and drove an electric current. B is perpendicular to the plane of the rail.

I

I

The EMF induced in the rod is:

The induced current flows through the moving rod

This current I in B will experience a magnetic force to the left:

So, in order to keep the wire moving at a constant speed v, we would need to apply a pulling force to the right.


Induced current in a circuit (rod moving to the left)

The figure shows a conducting wire sliding to the left (changed direction).

I

I

This induced current I in B will experience a magnetic force to the right:

So, in order to keep the wire moving at a constant speed v, we would need to apply a pulling force to the left.

A device that converts mechanical energy to electric energy is called a generator.

How can this device be called?

ConcepTest 4 Electrical generatorA) upB) downC) Into the screenD) Out of the screenE) To the right

An induced current flows clockwise as the metal bar is pushed to the right. The magnetic field points


Magnetic Flux


The Area Vector

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.


The Basic Definition of Flux (of air)

No air goes through the same loop if it lies parallel to the flow.

The flow is maximum through a loop that is perpendicular to the airflow.

Imagine holding a rectangular wire loop of area A = ab in front of a fan.

The volume of air flowing through the loop each second depends on the angle between the loop and the direction of flow.


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

⋅


Example: Determining flux

A square loop of wire encloses area A1.A uniform magnetic field B perpendicular to the loop extends over the area A2. What is the magnetic flux through the loop A1?

⋅ ⋅ ⋅

Area A1 Area A2Area A1 -A2

0

∥

A2 A2

B=constA=const

Theta=const,So the flux is const

ConcepTest 1 Electrical generator

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 2 Electrical generator II

A) yesB) no

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


Faraday’s Law


Recall Faraday’s experimentWe saw in the previous class that a moving magnet through the loop can cause an induced current. How can it be explained?


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:


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


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.


Example (Lenz’s Law)

I

The current in the straight wire is decreasing.

has CW direction

ConcepTest 3 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 4 Loop and Wire II


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

The induced emf around this loop is


What you should readChapter 33 (Knight)

Sections 33.3 33.4 33.5


Thank youSee you tomorrow

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L16 Ch33 Su15 - University of Massachusetts Lowell