Электрон влетает в пространство между обкладками плоского конденсторы параллельно обкладкам и посередине зазора между ними. При какой минимальной разности потенциалов между обкладками электрон не вылетит из конденстора, если его начальная скорость равна 2*10⁷м/с. Длина конденстора равна 10 см, ширина зазора между пластинами равна 1 см.
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(Some changes were made to the Google translate version for clarity)
An electron enters the space between the plates of a plane-parallel capacitor, parallel to the plates and in the middle of the gap between them. At what minimum potential difference between the plates will the electron not leave the capacitor if its initial velocity is equal to 2 * 10^7 m/sec? The coapacitor length is 10 cm; the width of the gap between the plates is 1 cm
An electron enters the space between the plates of a plane-parallel capacitor, parallel to the plates and in the middle of the gap between them. At what minimum potential difference between the plates will the electron not leave the capacitor if its initial velocity is equal to 2 * 10^7 m/sec? The coapacitor length is 10 cm; the width of the gap between the plates is 1 cm
It takes time T = L/v = 5*10^-7 s for an electron to pass through the plates. If, during that time, a strong enough electric field (V/d) is applied between the plates, the electron will strike one of the plates before it can pass through. If d is the plate separation, the requirement for NOT passing through is
e*(V/d)*(1/m)*(1/2)*T^2 > d/2
V > d^2*(m/e)*(L/v)^2
is the required voltage. Lower-case v is the velocity of the electron. m and e are the electron charge and mass, respectively.
e*(V/d)*(1/m)*(1/2)*T^2 > d/2
V > d^2*(m/e)*(L/v)^2
is the required voltage. Lower-case v is the velocity of the electron. m and e are the electron charge and mass, respectively.
ðåìÿ T = L / V = 5 * 10 ^ -7 S òðåáóåòñÿ äëÿ ýëåêòðîí ïðîõîäèò ÷åðåç ïëàñòèíû. Åñëè â òå÷åíèå ýòîãî âðåìåíè, äîñòàòî÷íî ñèëüíûì ýëåêòðè÷åñêèì ïîëåì (V / D) ïðèìåíÿåòñÿ ìåæäó ïëàñòèíàìè, ýëåêòðîííî óäàðèò îäíîé èç ïëàñòèí ïðåæäå ÷åì îí ñìîæåò ïðîéòè.
Åñëè D ÿâëÿåòñÿ ïëàñòèíà ðàçäåëåíèÿ, òðåáîâàíèÿ, íå ïðîõîäÿùèå ÷åðåç ÿâëÿåòñÿ
E * (V / D) * (1 / ì) * (1 / 2) * T ^ 2> D / 2
V> D ^ 2 * (M / E) * (L / V) ^ 2
ýòî íåîáõîäèìîå íàïðÿæåíèå. V-ñêîðîñòü ýëåêòðîíà. ì è å ìàññà è çàðÿä ýëåêòðîíà.
Åñëè D ÿâëÿåòñÿ ïëàñòèíà ðàçäåëåíèÿ, òðåáîâàíèÿ, íå ïðîõîäÿùèå ÷åðåç ÿâëÿåòñÿ
E * (V / D) * (1 / ì) * (1 / 2) * T ^ 2> D / 2
V> D ^ 2 * (M / E) * (L / V) ^ 2
ýòî íåîáõîäèìîå íàïðÿæåíèå. V-ñêîðîñòü ýëåêòðîíà. ì è å ìàññà è çàðÿä ýëåêòðîíà.
It seems that Jiskha cannot display my cyrillic characters, cut and pasted from Google.Translate. Sorry about that
Ýëåêòðîí ó÷àñòâóåò â äâóõ äâèæåíèÿõ:
ãîðèçîíòàëüíîì - ñ ïîñòîÿííîé ñêîðîñòüþ L =v•t,
è âåðòèêàëüíîì (ðàâíîóñêîðåííîì), ïðè êîòîðîì
ðàññòîÿíèå D/2 ïðîõîäèòñÿ çà òî æå âðåìÿ,
÷òî è âðåìÿ äâèæåíèÿ â ãîðèçîíòàëüíîì íàïðàâëåíèè,
D/2=at^2/2.
t=êâ.êîðåíü(D/a),
Ïî 2 çàêîíó Íüþòîíà ma=F(ýë)=eE=eU/d.
Óñêîðåíèå a =eU/mD.
t=êâ.êîðåíü(D^2•m/eU).
Îòñþäà L =v• êâ.êîðåíü(D^2•m/eU)
ãîðèçîíòàëüíîì - ñ ïîñòîÿííîé ñêîðîñòüþ L =v•t,
è âåðòèêàëüíîì (ðàâíîóñêîðåííîì), ïðè êîòîðîì
ðàññòîÿíèå D/2 ïðîõîäèòñÿ çà òî æå âðåìÿ,
÷òî è âðåìÿ äâèæåíèÿ â ãîðèçîíòàëüíîì íàïðàâëåíèè,
D/2=at^2/2.
t=êâ.êîðåíü(D/a),
Ïî 2 çàêîíó Íüþòîíà ma=F(ýë)=eE=eU/d.
Óñêîðåíèå a =eU/mD.
t=êâ.êîðåíü(D^2•m/eU).
Îòñþäà L =v• êâ.êîðåíü(D^2•m/eU)