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Exercise5

Horizontaldistance:DTheanglebetweenthehorizontalplaneandthelineconnectingthemicrophoneandtheairplaneis𝛼

tan 𝛼 =𝐻𝐷

Forashockwavewehave:

sin 𝛼 =𝑣!"#$%𝑣!"#$%!&'

Consequentlywehave:

𝐷 = 𝐻/tan sin!!𝑣!"#$%𝑣!"#$%!&'

Or,usingcos𝛼 = 1 − sin! 𝛼:

𝐷 =𝐻/

𝑣!"#$%𝑣!"#$%!&'

1 − 𝑣!"#$%𝑣!"#$%!&'

!

6

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Exercise9:EE/AU

a. Thetypeofdopingthatwasappliedisp-typeoracceptordoping,sinceitallowsforan

electroninthevalencebandtojumpintotheenergylevelofthedoping,thuscreatingahole

inthevalenceband.Thechargetransportisthereforedominatedbyholes.

b. Attemperaturesabove0Kelvin,theFermi-Diracdistributiontellsusthatelectronsexist

withanenergylevelbeyondtheFermilevel.TheFermilevelisatthetopofthevalence

band,sincethevalencebandisfullat0Kelvinandthereisnoconduction(isolator).An

electronwithhigherenergythantheFermilevelcanjumptothedopingenergyleveland

getstrappedthereatafixedpositioninthematerial,atthepositionofanacceptoratom,

whileitleavesaholeinthevalenceband.Thisholeisnowavailableforchargetransport.

Answers

a. ; is pointing to the right; is pointing upward, and therefore should be pointing into the paper (since 0).

b. The protons gain an energy Δ Δ ⇒

The speed is not changed by the magnetic field

c. Cyclotron orbit: ⇒

Ex. 5('8) s-T-l"'-1\:.-Tf:>\:_-(TN L

<A~ I =f r2ol110 / -k>r1,.lo. sht,e.{ : L=-rn. t-.

2 )

•. \. 1 ,t 't

_ .p , ..... ,

-f--¼,,,·'f li.:r,e>L,t' : L. '"'l.:"c =- J.::. °'-2-= Rc~-T~-- ~(JI1,,__ __

ay = RL~ (JI ) ---4 Tc.~,, R2 .T J RL ._

-----

~ ~ --- w rt • :w:a ""*" •..-i

-=}---- r~ - I .l ~ -- -.ij,"it""' ..J,.._ c .. /' t.'l>" , ~~~- ~ - ,, ;.....

~ 2.

_Ex .3 6MT - MW-\

0 L -~+x

I w Eg__- cc"'~~a10.. :[ T y.. = o

Tt~ (L-x) - 1,,/f = 0 (It)

\i) ii'\ {:rr) ~ (L-x)- {t) ·x = o

L ==) X

=I+(~)

---

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Zt:0

= o =\ - T:.Q +- ¼,I/ LL-OJ - o (Jr_,__\_

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I" I

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