electric fields , capacitance

7/26/2019 Electric Fields , Capacitance

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Electric Fields, Capacitance

Paper-2, As Level

June 2002

6 Two horizontal metal plates are situated !2 cm apart, as illustrated in Fi"! #!!

Fig. 6.1

The electric $ield %etween the plates is $ound to %e &!0'0()C*in the downward direction!

(a) (i) +n Fi"! #!, mar with a the plate which is at the more positive potential!

(ii) Calculate the potential di$$erence %etween the plates!

potential di$$erence . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! / &1

(b) etermine the acceleration o$ an electron %etween the plates, assumin" there is a

vacuum %etween them!

acceleration . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ms*2 &1

3#4

June 2005

6 Two parallel metal plates P and 6 are situated 7!0 cm apart in air, as shown in Fi"! #!!


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Fig. 6.1

Plate 6 is earthed and plate P is maintained at a potential o$ #0 /!

(a) (i) +n Fi"! #!, draw lines to represent the electric $ield in the re"ion %etween the

plates! 21

(ii) 8how that the ma"nitude o$ the electric $ield %etween the plates is 2!0 ' 0&/m*!

1

(b) A dust particle is suspended in the air %etween the plates! The particle has char"es o$

!2 ' 0*5C and *!2 ' 0*5C near its ends! The char"es ma9 %e considered to %e

point char"es separated %9 a distance o$ 2!5 mm, as shown in Fi"! #!2!

Fig. 6.2

The particle maes an an"le o$ &5: with the direction o$ the electric $ield!

(i) +n Fi"! #!2, draw arrows to show the direction o$ the $orce on each char"e due to

the electric $ield! 1

(ii) Calculate the ma"nitude o$ the $orce on each char"e due to the electric $ield!

$orce . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ) 21

(iii) etermine the ma"nitude o$ the couple actin" on the particle!


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couple . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! )m 21

(iv) 8u""est the su%se;uent motion o$ the particle in the electric $ield!

2(6)

June 200=

2 (a) e$ine electric field strength!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1

(b) Two $lat parallel metal plates, each o$ len"th 2!0 cm, are separated %9 a distance o$

!5 cm, as shown in Fi"! 2!!

Fig. 2.1


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The space %etween the plates is a vacuum!

The potential di$$erence %etween the plates is 20 /! The electric $ield ma9 %e assumed

to %e uni$orm in the re"ion %etween the plates and zero outside this re"ion!

Calculate the ma"nitude o$ the electric $ield stren"th %etween the plates!

$ield stren"th . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!) C* 1

(c) An electron initiall9 travels parallel to the plates alon" a line mid-wa9 %etween the plates,

as shown in Fi"! 2!! The speed o$ the electron is 5!0 ' 0=m s*!

For the electron %etween the plates,

(i) determine the ma"nitude and direction o$ its acceleration,

acceleration . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!m s*2

direction !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (1

(ii) calculate the time $or the electron to travel a horizontal distance e;ual to the len"th

o$ the plates!

time . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!s 1

(d) >se 9our answers in (c) to determine whether the electron will hit one o$ the plates oremer"e $rom %etween the plates!

&1


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&324

)ov 2002

6 An electron travellin" horizontall9 in a vacuum enters the re"ion %etween two horizontal


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metal plates, as shown in Fi"! #!!

Fig. 6.1

The lower plate is earthed and the upper plate is at a potential o$ (00/! The separation o$

the plates is 0!70 cm!

The electric $ield %etween the plates ma9 %e assumed to %e uni$orm and outside the plates

to %e zero!

(a) +n Fi"! #!,

(i) draw an arrow at P to show the direction o$ the $orce on the electron due to the

electric $ield %etween the plates,

(ii) setch the path o$ the electron as it passes %etween the plates and %e9ond them!

&1

(b) etermine the electric $ield stren"thE%etween the plates!

E .


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acceleration .

Fi"!5!

A potential di$$erence o$ (50/ is maintained %etween the plates %9 means o$ a %atter9!

(a) 3i4 +n Fi"!5!, draw an arrow to indicate the direction o$ the electric $ield %etweenplates A and !


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3ii4 Calculate the electric $ield stren"th %etween A and !

$ield stren"th .

speed .


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)ov 2005

6 Two horizontal metal plates D and are at a distance 0!=5 cm apart! A positivel9 char"ed

particle o$ mass B!# ' 0*5" is situated in a vacuum %etween the plates, as illustrated in

Fi"! #!!

Fig. 6.1

The potential di$$erence %etween the plates is adusted until the particle remains stationar9!

(a) 8tate, with a reason, which plate, D or , is positivel9 char"ed!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 21

(b) The potential di$$erence re;uired $or the particle to %e stationar9 %etween the plates is

$ound to %e #&0 /! Calculate

(i) the electric $ield stren"th %etween the plates,

$ield stren"th .


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June 200=& Two char"ed points A and are separated %9 a distance o$ #!0 cm, as shown in Fi"! &!!

Fig. 3.1

The variation with distance d $rom A o$ the electric $ield stren"thE alon" the line A is

shown in Fi"! &!2!

Fig. 3.2

An electron is emitted with ne"li"i%le speed $rom A and travels alon" A!

(a) 8tate the relation %etween electric $ield stren"thE and potential V!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

(b) The area %elow the line o$ the "raph o$ Fi"! &!2 represents the potential di$$erence

%etween A and !

>se Fi"! &!2 to determine the potential di$$erence %etween A and !


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potential di$$erence .


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(c) >se 9our answer to (b) to calculate the speed o$ the electron as it reaches point !

speed .

Fig. 6.1

The diode is ideal! The -plates o$ a cathode-ra9 oscilloscope 3c!r!o!4 are connected %etween

points A and !

(a) (i) Calculate the ma@imum potential di$$erence across the diode durin" one c9cle!


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potential di$$erence .


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$raction .

electrical %readown o$ the air occurs!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 21

June 2005


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5 An isolated conductin" sphere o$ radius r is "iven a char"e Q! This char"e ma9 %e

assumed to act as a point char"e situated at the centre o$ the sphere, as shown in Fi"! 5!!

Fig. 5.1

Fi"! 5!2! shows the variation with distancex $rom the centre o$ the sphere o$ the potential V

due to the char"e Q!

Fig. 5.2

(a) 8tate the relation %etween electric $ield and potential!

(b) >sin" the relation in (a), on Fi"! 5!& setch a "raph to show the variation with distance x

o$ the electric $ieldE due to the char"e Q!

&1

Fig. 5.3

8 (a) e$ine capacitance!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1

(b) (i) +ne use o$ a capacitor is $or the stora"e o$ electrical ener"9!

rie$l9 e@plain how a capacitor stores ener"9!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 21

(ii) Calculate the chan"e in the ener"9 stored in a capacitor o$ capacitance 200 KF

when the potential di$$erence across the capacitor chan"es $rom 50 / to 5 /!

ener"9 chan"e . !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! J &1

electric fields , capacitance

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