Department of Physics and Applied Physics95.144 Danylov Lecture 18

Lecture 18

Chapter 33

Induced Fields

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

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

Physics II

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Faraday’s Law (leftovers)

Department of Physics and Applied Physics95.144 Danylov Lecture 18

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:

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Jumping Ring DemonstrationWith a metal ring in place, turn on the switch. The solid ring will jump. Why?

I increases

has CW direction

Let’s look at a force on the ring:

This components cancel each other

Vertical components add each other

Thus, the net force is up and the ring jumps

Department of Physics and Applied Physics95.144 Danylov Lecture 18

An Alternating-Current Generator

Φcos cos sin

Department of Physics and Applied Physics95.144 Danylov Lecture 18

GeneratorsA generator is a device that transforms mechanical energy into

electric energy.

A generator inside a hydroelectric dam uses electromagnetic induction to convert the mechanical energy of a spinning turbine

into electric energy.

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Induced Electric Field

Let’s reformulate Faraday’s Law in terms of

Φ

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Induced Electric FieldConsider a conducting loop in an increasing uniform magnetic field.

CCW

So, according to Lenz’s law, there is an induced current in the counterclockwise direction.If there is a current, there must be something that acts on the charge carriers to make them move, so we infer that there must be an induced electric field tangent to the loop at all points

sdEVVVf

iif

Combine these ∆V or Ɛ (emf) over the closed loop:

dtdsdEV m

General form of Faraday’s law

1) A changing magnetic field produces an electric field!!!

2) The conducting loop is not necessary. The electric field arise whether or not circuits are present.

The space is filled with an induced electric fields.

Amazing things:

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Two types of E

Thus, now we know two types of electric field:1) Coulomb electric field is created by a charge q:

Coulomb el. field lines start/stop on charges

Induced el. field lines form closed loops

2) Induced electric field by changing magnetic field:

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Faraday’s law

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Where can we see a case like that?

In a solenoid

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Induced Electric Field in a Solenoid The current through the solenoid

creates an upward pointing magnetic field.

As the current is increasing, B is increasing, so it must induce an electric field.

We could use Lenz’s law to determine that if there were a conducting loop in the solenoid, the induced current would be clockwise.

The induced electric field must therefore be clockwise around the magnetic field lines.

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Induced Electric Field in a Solenoid

ConcepTest Faraday’s Law

The magnetic field is decreasing. Which is the induced electric field?

E. There’s no induced field in this case.

The field is the same direction as induced current would flow if there were a loop in the field.

CCWImagine a loop

CCW

Department of Physics and Applied Physics95.144 Danylov Lecture 18

InductorsYou remember, capacitors store potential energy in

a form of an electric field.

Now, inductors (solenoids) store potential energy in a form of a magnetic field.

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Inductance (definition)Consider a solenoid of N turns with current I.

The total magnetic flux is I

Φ ~

The coefficient of proportionality is called inductance, L

The SI unit of inductance is the henry, defined as:1 henry = 1 H = 1 Wb/A = 1 T m2/A

The circuit symbol for an ideal inductor is .

The solenoid’s magnetic field passes through the coils, establishing a flux.

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Let’s find solenoid inductanceConsider a solenoid of N turns with current I.

Recall (Lecture 14)

Φ

You see, solenoid inductance depends only on its geometry

Φ Φ ∙ ∥

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Potential Difference across an Inductor

Φ

Δ

Potential difference across an inductor

Note The magnitude of I has no effect on ΔV, only the rate of change of I counts.

If current increases, 0 Δ 0

If current decreases, 0 Δ 0

If current is constant,I=const Δ 0

The induced V decreases if the current is increasing

_

The induced V increases if the current is decreasing+_

Δ

initial final

initial final

1) Current I1

2) Current I2

3) They are changing at the same rate

4) Not enough information to tell

Which current is changing more rapidly?

ConcepTest Inductor

41

22

Department of Physics and Applied Physics95.144 Danylov Lecture 18

What you should readChapter 33 (Knight)

Sections 33.6 33.7 (skip “Transformers”) 33.5

Department of Physics and Applied Physics95.144 Danylov Lecture 18

Thank youSee you on Friday