multipole expansion - smu physics...dipole moment - off center d +2q-q what is the dipole moment of...

MULTIPOLE EXPANSION

What is the magnitude of the dipole

moment of this charge distribution?

A) qd

B) 2qd

C) 3qd

D) 4qd

E) It's not determined

p = qiri

i

å

Dipole moment - off center

d

+2q

-q

What is the dipole moment of this system?

(Note: it is NOT overall neutral!)

x0

p = qiri

i

å

A) qd

B) 2qd

C)3

2qd

D) 3 qd

E) Something else

(or, not defined)!

Dipole moment - off center

d/2

d

+2q

-q

What is the dipole moment of this system?

(Note: same as last question, just shifted in z!)

d/2

0x

r1

r2

p = qiri

i

å

A) qd

B) 2qd

C)3

2qd

D) 3 qd

E) Something else

(or, not defined)!

Dipole moment - off center

x

y

r1

r2

d

+q

-q i i

i

q r ?=å

A) + qd

B) - qd

C) zero

D) None of these, it's more complicated now!

Which of the following is correct (and "coordinate

free")?

A) B)

C) D)

E) None of these

A small dipole (dipole moment p=qd) points

in the z direction.

We have derived V(r ) »1

4pe0

qd cosq

r2=

1

4pe0

qd z

r3

V (

r ) =1

4pe0

p × ˆ r

r2

V (

r ) =1

4pe0

p ×

r

r2

V (

r ) =1

4pe0

p ́ ˆ r

r2

V (

r ) =1

4pe0

p × ˆ r

r3

You have a physical dipole, +q and -q

a finite distance d apart.

When can you use the expression:

A) This is an exact expression everywhere.

B) It's valid for large r

C) It's valid for small r

D) ?

V (

r ) =1

4pe0

p × ˆ r

r2

You have a physical dipole, +q and -q,

a finite distance d apart.

When can you use the expression

A) This is an exact expression everywhere.

B) It's valid for large r

C) It's valid for small r

D) ?

Electric Dipole Radiation

Heinrich Hertz

(1857 – 1894) German physicist, first conclusively

proved the existence of the electromagnetic

waves theorized by James Clerk Maxwell

Asked about the applications of his discoveries,

Hertz replied, "Nothing, I guess."

Which charge distributions below produce

a potential which looks like C/r2 when you

are far away?

E) None of these, or more than one of these!

(Note: for any which you did not select, how

DO they behave at large r?)

Which charge distributions below produce

a potential which looks like C/r2 when you

are far away?

E) None of these, or more than one of these!

(Note: for any which you did not select, how

DO they behave at large r?)

In which situation is the dipole term the

leading non-zero contribution to the

potential?

A) A and C

B) B and D

C) only E

D) A and E

E) Some other combo

r(r)

+r0

s =s 0 cos(q)

V(z) =1

4peo

l dz '

Âò

=if z>0

1

4pe0

ldz '

(z - z ')z'=-d

z'=0

ò

=l

4pe0

(-)ln(z - z ') |-d

0

=l

4pe0

ln(z + d

z)

x

z

-d l

dz’ z’

Â