Inductors

PH 203

Professor Lee Carkner

Lecture 20

Ring in Solenoid If the current flows clockwise through the solenoid,

the B field inside is straight down To get maximum flux, the ring should face up

(parallel with the coils) We need to find the flux through the loop before and

after the current is switched off = BA cos = BA B = 0nI = (4X10-7)(1000)(10) = 0.0126 T

A = (0.1)(0.1) = 0.01 m2

Current in Ring

= BA = (0.0126)(0.01) = 1.26 X 10-4 Wb In 1 second the flux goes to 0 = (1.26 X 10-4) - (0) = 1.26 X 10-4

t = 1 = -N(/t) = (1)(1.26 X 10-4) = 1.26 X 10-4 V V = iR or i = /R = 1.26 X 10-4/10 i = 1.26 X 10-5 A

Applied Induction

You connect a source of motion to a magnet The changing flux produces a changing current

Can easily amplify and move the current Many applications in music

Microphone

Electric Guitar

Induction Devices Microphone

Speaker

Electric guitar Pickup magnet magnetizes string, the motion of which

induces current

Tape recorders and players The tape is magnetized such that when it passes the tape

heads it induces a current

How Does Induction Work?

If we move the wire through a B field the

electrons now have a velocity

This deflection produces an imbalance of charge

Finding emf

= -N(d/dt) But the magnetic flux depends on the changing current and

the properties of the coil

= -L(di/dt)

where the constant of proportionality L is the inductance

Inductance The unit of inductance is the henry,

Equating the two expressions for

= L(di/dt) = N(d/dt)L = N(d/di)

Inductance is a property of the circuit element Like resistance or capacitance

Solenoid Inductance To find L, we need a relationship between and I for a

solenoid

Flux in general: = BA cos or = BA

B = 0(N/l)i or i = Bl/(0N)

L = N(d/di) = N/i = NBA0N/Bl = 0N2A/l

L = 0n2Al Note:

N is number of turns, n is number of turns per meter

Inductors

In a circuit any element with a high inductance is represented by an inductor

We will assume that the rest of the circuit has negligible inductance

Symbol is a spiral:

Motional emf

If we make the loop larger or smaller, or move it in or out of a field, we will induce a potential remember emf is a potential difference (or voltage)

How does motion in a field translate to voltage?

Motional emf - Derived

Consider a conductor of length L sliding on a frame with velocity v

but x = vt, so A = Lvt

/t = BA/t = (BLvt)/t = BLv

X

B field into page

v

x

L

x in time t

A

Motional emf -- Direction

If the area decreases, the flux decreases and thus the induced B field is in the same direction as the original

Motional emf Energy

How is energy related to motional emf? The loop feels a magnetic force you have to

overcome

The energy goes into the electrical energy of the current in the loop

P = i2R

Power and Motional emf

Since = BLv and = iR, we can write:

i = BLv/R

P = B2L2v2/R Large loops with low resistance moving

fast in a large magnetic field will have a lot of electrical energy and thus require more work input

Force on Eddy

Currents

Eddy Currents Imagine a loop moving out of a magnetic field As the field through the loop drops, it induces a field in

the same direction

If the object is not a loop, circular currents can still be induced which have the same effect Called eddy currents

Metal objects moving through a magnetic field will be slowed

Next Time

Read 30.8-30.12 Problems: Ch 30, P: 21, 29, 31, 48, 51

What is the direction of current in the loop from the PAL (seen from top down)?

A) clockwise

B) counterclockwise

C) left

D) right

E) down

A ring undergoes thermal expansion while in a uniform magnetic field. If the current induced in the loop is clockwise, what is the direction of the magnetic field?

A) left

B) right

C) into the page

D) out of the page

E) counterclockwise

A bar magnet held north pole up is dropped straight down through a face up coil of wire. What is the direction of the current in the coil as the magnet enters and leaves the coil?

A) clockwise, counterclockwise

B) counterclockwise, clockwise

C) clockwise, clockwise

D) counterclockwise, counterclockwise

E) no current is induced