Displacement Current and EM Waves - Lecture Slides | PHYS 212, Study notes of Physics

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Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide

Physics 212

Physics 212

Lecture 21

Lecture 21

0

40 30 20 10

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

2

Some of your comments:

Some of your comments:

These equations just keep getting more and more confusing. It would be helpful if they wereexplained more as far as how to use them. deriving the displacement current and the relationship between electric and magnetic fields.2. Everything. You said this would get easier but this might be the This prelecture was fascinating! Please just go over it all again. It's so awesome that electricfields are so intrinsically related to magnetic fields. Considering changing my major? Verymuch so.

hardest one yet. I don't get it..

For the derivation part, why did we use fardays

law for Dx

and ampere's law for Dy. I mean, wasn't

too much work for credit hours given in this class, seriously needs to be looked into Explain, in-depth, Einstein's theory of relativity in 2 minutes. Go. how can the speed of light be the same in any inertial referencethat just a lucky guess that magnetism movies in the y-direction? Maybe I missed something, but itseems like that one was just swept under the carpet. Also, this EM wave stuff is kind of blowing mymind. Can we, like, chill on this for a few days so i can wrap my head around it? Gracias, gue.

frame? what if you're going the

Is this for real? Like I opened the prelecture and just went "Ahspeed of light? shouldn't the speed of light be 0 in that reference frame? this is some crazy sh*tman.

buhuh?" Please make this

simple. And if you could make TAM212 simple I'd like that too I liked the old Ampere's Law, WHY DID YOU HAVE TO CHANGE IT!!!!!!!!!!!

More cowbell please.

steve

nash

is canadian, like mats! could you invite him to class?

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

4

0

0

Q

E

A

σ ε

ε

=

=

0

Q

EA

ε

Φ

=

=

0

Q

ε

=

Φ

0

dQ

d

dt

dt

ε

Φ

=

But: so far we have ignored But: so far we have ignored

dQ/dt dQ/dt

in the capacitor in the capacitor

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

5

Displacement Current Displacement Current

Real Current:

Charge Q passes through area A in

time t:

Displacement Current:

Electric flux through area A changes in

time

dQ

I

dt

=

0

E

D

d

I

dt

ε

Φ

=

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

7

Calculation Calculation

Switch S has been open a long time when at t = 0, it is closed.Capacitor C

has circular plates of radius R. At time t

= t

1

, a

current I

1

flows in the circuit and the capacitor carries

charge Q

1

S

S

R

R

a a

V

V

C

C

● ●

R R

r r

● ●

r r

I

1

Q

1

c c

d d

Compare the magnitudes of the B fields at points c and d.

(A)

B

c

< B

d

(B) B

c

= B

d

(C) B

c

> B

d

What is the difference?

Apply (modified) Ampere’s Law

point c:

I(enclosed) = I

1

X

rr

point d:

I

D

(enclosed) < I

1

r r

R R

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

8

Calculation Calculation

Switch S has been open a long time when at t = 0, it is closed.Capacitor C

has circular plates of radius R. At time t

= t

1

, a

current I

1

flows in the circuit and the capacitor carries

charge Q

1

S

S

R

R

a a

V

V

C

C

RR

r r

●●

I

1

Q

1

d d

What is the magnitude of the electric field between the plates?

(A)

(B)

(C)

(D)

R R

1 2

0

Q

E

R

EE

0

E

σ ε

=

1

2

0

Q

E

R

ε π

2

1

0

Q

R

E

π ε

1

0

Q

E

ε

1

Q

E

r

0

E

σ ε

1

1

2

Q

Q

A

R

σ

π

Q Q

1 1

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

10 10

Calculation Calculation

Switch S has been open a long time when at t = 0, it is closed.Capacitor C

has circular plates of radius R. At time t

= t

1

, a

current I

1

flows in the circuit and the capacitor carries

charge Q

1

S

S

R

R

a a

V

V

C

C

RR

r r

●●

I

1

Q

1

d d

What is the displacement current enclosed by circle of radius r?

(A)

(B)

(C)

(D)

r r

R R

EE

2

1

2

D

r

I

I

R

=

0

E

D

d

I

dt

ε

Φ

=

2

1

2

dQ

r

dt

R

=

2

1

2

r

I

R

=

2

1

2

D

R

I

I

r

=

2

1

2

D

r

I

I

R

=

1

D

r

I

I

R

=

1

D

R

I

I

r

=

2

1

2

0

E

Q r

R

0

E

D

d

I

dt

ε

Φ

=

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

11 11

Calculation Calculation

Switch S has been open a long time when at t = 0, it is closed.Capacitor C

has circular plates of radius R. At time t

= t

1

, a

current I

1

flows in the circuit and the capacitor carries

charge Q

1

S

S

R

R

a a

V

V

C

C

RR

r r

●●

I

1

Q

1

d d

What is the magnitude of the B field at radius r?

(A)

(B)

(C)

(D)

r r

R R

EE

2

1

2

D

r

I

I

R

=

0

1

2

I

r

B

R

0

1

I

B

R

0

1

I

B

r

0

1

2

I

R

B

r

Ampere’s Law:

0

D

B d

I

I

μ

∫

G

G

i

A

v

2

0

1

2

2

0

r

B

r

I

R

π

μ

⎛

⎞

⋅

=

⎜

⎟

⎝

⎠

0

1

2

I

r

B

R

μ

π

0

D

B d

I

I

μ

∫

G

G

i

A

v

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

14 14

Follow Follow

Up Up

Switch S has been open a long time when at t = 0, it is closed.Capacitor C

has circular plates of radius R. At time t

= t

1

, a

current I

1

flows in the circuit and the capacitor carries

charge Q

1

What is the time dependence of the magnetic field B at aradius r between the plates of the capacitor?

S

S

R

R

a a

V

V

C

C

B

at fixed r

is proportional to the current I

Close switch: V

C

fl

I

= V/R

a

(maximum)

I

exponentially decays with time constant

τ

= R

a

C

0

1

1

2

I

r

B

R

(A)

(B)

(C)

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

15

We learned about waves in Physics 211

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

17

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

18

Physics 212 Lecture 21, Slide Physics 212 Lecture 21, Slide

20

0

60 50 40 30 20 10

Preflight

E

x

= E

0

sin(kz-

ω

t)

All three are at the same distance Z so the fields

All three are at the same distance Z so the fields

are all equal.

are all equal.

Physics 212 Lecture 21, SlidePhysics 212 Lecture 21, Slide

21

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