1. General Certificate of Education
Advanced Level Examination
January 2010
Physics A PHYA4
Unit 4 Fields and Further Mechanics
Data and Formulae Booklet
'$7$
)81'$0(17$/ &2167$176 $1' 9$/8(6
4XDQWLW 6PERO 9DOXH 8QLWV
VSHHG RI OLJKW LQ YDFXR F ×
P V±
SHUPHDELOLW RI IUHH VSDFH µR π × ± + P±
SHUPLWWLYLW RI IUHH VSDFH εR × ± ) P±
FKDUJH RI HOHFWURQ H ± × ±
±
WKH 3ODQFN FRQVWDQW K × -V
JUDYLWDWLRQDO FRQVWDQW * × ± 1 P NJ±
WKH $YRJDGUR FRQVWDQW 1$ × PRO±
PRODU JDV FRQVWDQW 5 - .± PRO±
WKH %ROW]PDQQ FRQVWDQW N × ± - .±
WKH 6WHIDQ FRQVWDQW σ × ± : P± .±
WKH :LHQ FRQVWDQW α × ± P.
HOHFWURQ UHVW PDVV
PH × ± NJ
HTXLYDOHQW WR î ± X

2. HOHFWURQ FKDUJHPDVV UDWLR HPH × NJ±
SURWRQ UHVW PDVV
PS

3. × ± NJ
HTXLYDOHQW WR X

4. SURWRQ FKDUJHPDVV UDWLR HPS × NJ±
QHXWURQ UHVW PDVV
PQ

5. × ± NJ
HTXLYDOHQW WR X

6. JUDYLWDWLRQDO ILHOG VWUHQJWK J 1 NJ±
DFFHOHUDWLRQ GXH WR JUDYLW J P V±
DWRPLF PDVV XQLW
X × ± NJ
X LV HTXLYDOHQW WR 0H9

7. *(20(75,$/ (48$7,216
DUF OHQJWK Uθ
$6752120,$/ '$7$ FLUFXPIHUHQFH RI FLUFOH π U
%RG 0DVVNJ 0HDQ UDGLXVP DUHD RI FLUFOH π U
6XQ î î VXUIDFH DUHD RI FOLQGHU π UK
(DUWK î î YROXPH RI FOLQGHU π UK
DUHD RI VSKHUH π U
YROXPH RI VSKHUH π U
This insert page should not be sent to the examiner
INSERT TO WMP/Jan10/PHYA4 Turn over ᮣ

8. 2
$6 )2508/$(
(/(75,,7
FXUUHQW DQG ǻ4 : 9
, 9 5
3$57,/( 3+6,6 SG ǻW 4 ,
(
HPI İ= İ = , 5 + U

9. 5HVW HQHUJ YDOXHV 4
UHVW HQHUJ
FODVV QDPH VPERO UHVLVWRUV LQ VHULHV 5 5 5 5 «
0H9
SKRWRQ SKRWRQ γ
UHVLVWRUV LQ SDUDOOHO = + + +
OHSWRQ QHXWULQR YH 5 5 5 5
Yµ 5$
UHVLVWLYLW ȡ=
HOHFWURQ H /
PXRQ µ 9
SRZHU 3 9, , 5
PHVRQV π PHVRQ π 5
π , 9
DOWHUQDWLQJ FXUUHQW ,UPV 9UPV
. PHVRQ .
. 0(+$1,6
EDURQV SURWRQ S PRPHQWV PRPHQW )G
QHXWURQ Q YHORFLW DQG ∆V ∆Y
Y D
DFFHOHUDWLRQ ∆W ∆W
X + Y

10. HTXDWLRQV RI PRWLRQ Y X DW V W
DW
Y X DV V XW
3URSHUWLHV RI TXDUNV
DQWLTXDUNV KDYH RSSRVLWH VLJQV IRUFH ) PD
EDURQ ZRUN HQHUJ DQG : ) V FRV ș
WSH FKDUJH VWUDQJHQHVV
QXPEHU SRZHU (. ò P Y ǻ(3 PJǻK
∆:
X H 3 3 )Y
∆W
XVHIXO RXWSXW SRZHU
G ± H HIILFLHQF
LQSXW SRZHU
0$7(5,$/6
V ± H
GHQVLW P +RRNH¶V ODZ ) N ǻ/
ȡ
9
)
3URSHUWLHV RI /HSWRQV RXQJ WHQVLOH VWUHVV WHQVLOH VWUHVV
PRGXOXV $
WHQVLOH VWUDLQ
OHSWRQ QXPEHU ǻ/
WHQVLOH VWUDLQ
HQHUJ /
SDUWLFOHV Hí νH µí νµ ( )ǻ/
VWRUHG
:$9(6
DQWLSDUWLFOHV H Ȟ H µ Ȟ ȝ ±
ZDYH VSHHG F IȜ SHULRG 7
I
3KRWRQV DQG (QHUJ /HYHOV IULQJH Ȝ' GLIIUDFWLRQ G VLQ ș QȜ
VSDFLQJ Z JUDWLQJ
SKRWRQ HQHUJ ( KI KF λ V
SKRWRHOHFWULFLW KI φ (. PD[

11. F
UHIUDFWLYH LQGH[ RI D VXEVWDQFH V Q
HQHUJ OHYHOV KI( ± ( FV
K K
GH %URJOLH :DYHOHQJWK Ȝ= = IRU WZR GLIIHUHQW VXEVWDQFHV RI UHIUDFWLYH LQGLFHV Q DQG Q
S PY
ODZ RI UHIUDFWLRQ Q VLQ ș Q VLQ ș
Q
FULWLFDO DQJOH VLQ șF IRU Q ! Q
Q
INSERT TO WMP/Jan10/PHYA4

12. 3
$ )2508/$(
020(1780 HOHFWULF SRWHQWLDO ǻ: 4ǻ9
∆PY

13. 4
IRUFH ) 9
∆W ʌİ U U
4
LPSXOVH ) ǻW ǻPY

14. FDSDFLWDQFH
9
,58/$5 027,21 GHFD RI FKDUJH 4 4H±W5
Y
DQJXODU YHORFLW ω WLPH FRQVWDQW 5
U
ω ʌ I 4
FDSDFLWRU ( 49 9
Y HQHUJ VWRUHG
FHQWULSHWDO DFFHOHUDWLRQ D ω U
U
PY 0$*1(7, ),(/'6
FHQWULSHWDO IRUFH ) Pω U ) %, O
U IRUFH RQ D FXUUHQW
26,//$7,216 IRUFH RQ D PRYLQJ FKDUJH ) %4Y
DFFHOHUDWLRQ D íπI

15. [ PDJQHWLF IOX[ Ɏ %$
GLVSODFHPHQW [ $ FRV πI W

16. PDJQHWLF IOX[ OLQNDJH 1Ɏ %$1
Y = ± ʌI $ − [ PDJQLWXGH RI LQGXFHG HPI ǻΦ
VSHHG İ 1
ǻW
PD[LPXP VSHHG YPD[ πI$ 1Ɏ %$1 FRV ș
HPI LQGXFHG LQ D URWDWLQJ FRLO
PD[LPXP DFFHOHUDWLRQ DPD[ πI

17. $ İ %$1ω VLQ ω W
P 1 V 9V
IRU D PDVVVSULQJ VVWHP 7 ʌ WUDQVIRUPHU HTXDWLRQV =
N 1 S 9S
O , V 9V
IRU D VLPSOH SHQGXOXP 7 ʌ HIILFLHQF
J , S 9S
*5$9,7$7,21$/ ),(/'6 5$',2$7,9,7 $1' 18/($5 3+6,6
IRUFH EHWZHHQ WZR * P P WKH LQYHUVH VTXDUH ODZ IRU Ȗ N
) ,
PDVVHV U UDGLDWLRQ [
JUDYLWDWLRQDO ILHOG ) UDGLRDFWLYH GHFD ∆1
J ± Ȝ 1 1 1RHλW
VWUHQJWK P ∆W
PDJQLWXGH RI *0 DFWLYLW $ Ȝ1
JUDYLWDWLRQDO ILHOG J
U OQ
VWUHQJWK LQ D UDGLDO ILHOG KDOIOLIH 7ò
JUDYLWDWLRQDO SRWHQWLDO ǻ: Pǻ9 Ȝ
*0
9 ± QXFOHDU UDGLXV 5 U $
U
∆9
J ± HQHUJPDVV HTXDWLRQ ( P F
∆U
*$6(6 $1' 7+(50$/ 3+6,6
(/(75, ),(/'6 $1' $3$,7256
JDV ODZ S9 Q57
IRUFH EHWZHHQ WZR SRLQW 4 4
) S9 1N7
FKDUJHV ʌİ U
IRUFH RQ D FKDUJH ) (4 NLQHWLF WKHRU PRGHO S9 1 P FUPV

18. ILHOG VWUHQJWK IRU D 9 NLQHWLF HQHUJ RI JDV 57
( P FUPV

19. N7
XQLIRUP ILHOG G PROHFXOH 1$
4 HQHUJ WR FKDQJH
ILHOG VWUHQJWK IRU D UDGLDO ( 4 PFǻ7
WHPSHUDWXUH
ILHOG ʌİ U
HQHUJ WR FKDQJH VWDWH 4 PO
INSERT TO WMP/Jan10/PHYA4
Turn over ᮣ

20. 4
237,216 )2508/$(
$67523+6,6 WRUTXH 7 ,Į
DVWURQRPLFDO XQLW î P DQJXODU PRPHQWXP DQJXODU PRPHQWXP ,ω
OLJKW HDU î P ZRUN GRQH : 7ș
SDUVHF $8 î P O U SRZHU 3 7ω
+XEEOH FRQVWDQW + NP V± 0SF± WKHUPRGQDPLFV 4 ǻ8 :
: Sǻ9
OHQV HTXDWLRQ
I X Y DGLDEDWLF FKDQJH S9Ȗ FRQVWDQW
DQJOH VXEWHQGHG E LPDJH DW HH LVRWKHUPDO FKDQJH S9 FRQVWDQW
0
DQJOH VXEWHQGHG E REMHFW DW XQDLGHG HH KHDW HQJLQHV
I : 4LQ − 4RXW
LQ QRUPDO DGMXVWPHQW 0 HIILFLHQF
IH 4LQ 4LQ
Ȝ 7 + − 7
UHVROYLQJ SRZHU ș§ PD[LPXP HIILFLHQF
' 7+
G ZRUN GRQH SHU FFOH DUHD RI ORRS
PDJQLWXGH HTXDWLRQ P±0 ORJ
LQSXW SRZHU FDORULILF YDOXH î IXHO IORZ UDWH
LQGLFDWHG SRZHU DUHD RI S9 ORRS

21. î QR RI FFOHV
:LHQ¶V ODZ ȜPD[ 7 P .
SHU VHFRQG

22. î QXPEHU RI FOLQGHUV
+XEEOH ODZ Y +G RXWSXW RI EUDNH SRZHU 3 7 ω
6WHIDQ¶V ODZ 3 ı $ 7 IULFWLRQ SRZHU LQGLFDWHG SRZHU ± EUDNH SRZHU
∆I ∆Ȝ Y KHDW SXPSV DQG UHIULJHUDWRUV
'RSSOHU VKLIW IRU Y F ] ±
I Ȝ F 4RXW 4RXW
UHIULJHUDWRU 23UHI
*0 : 4LQ − 4RXW
6FKZDU]VFKLOG UDGLXV 5V
F 4LQ 4LQ
KHDW SXPS 23KS
0(',$/ 3+6,6 : 4LQ − 4RXW
7851,1* 32,176 ,1 3+6,6
OHQV HTXDWLRQV 3
I
H9
Y HOHFWURQV LQ ILHOGV )
P G
X
= + ) %HY
I X Y
, PY
LQWHQVLW OHYHO LQWHQVLW OHYHO ORJ U
, %H
DEVRUSWLRQ , ,H±ȝ[ ò PY H9
ȝ 49
ȝP PJ
ȡ G
$33/,(' 3+6,6 ) ʌ Ș U Y
PRPHQW RI LQHUWLD , ȈPU
ZDYH SDUWLFOH GXDOLW F
ȝ İ
DQJXODU NLQHWLF HQHUJ (N ,ω
HTXDWLRQV RI DQJXODU K K
Ȝ
PRWLRQ ω ω Į W S PH9
VSHFLDO P F
ω ω Įș UHODWLYLW ( PF
§ Y ·
ș ωW ĮW ¨ − ¸
¨ F ¸
© ¹
ș ò Ȧ Ȧ

23. W
−
§ Y · § Y ·
O O ¨ − ¸ W W ¨ − ¸
¨ F ¸ © F ¹
© ¹
INSERT TO WMP/Jan10/PHYA4