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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+(~)
---
ff~- ~ ---- " ll : T -+T -'~ ' .re .... r -W-, (I' A b ~ ________::_:__:_t._ 'A ;
Zt:0
= o =\ - T:.Q +- ¼,I/ LL-OJ - o (Jr_,__\_
µ • I -- / a_ ----+ --"'--=r ;r =------J/· .. ) '------"M..._,_ [ 1r). : -T '. r, + ( w -~ )( L - o 1 ~ hlLL- D ) + I' ..0-0 · A ' r1 ' • , , ;;,.
I" I
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