Kudziwa mphamvu yamagetsi pogwiritsa ntchito lamulo la Gauss

Malo amagetsi chifukwa cha chaji imodzi

Kuwerengera munda wamagetsi Chopangidwa ndi mphamvu imodzi yokha, gawo loyamba ndikusankha pamwamba pa Gaussian wa radius r pomwe pakati pa mphamvuyo pali mphamvu imodzi yokha. Malo a pamwamba pa mphamvuyo ndi 4.r².

Mphamvu yamagetsi yochokera pakati pa mpira imalowa mozungulira pamwamba pa mpira kotero kuti njirayo kutuluka kwa magetsi ndi Φ = E A. Fomula Lamulo la Gauss ndi Φ = Q / ε_o

Mphamvu yamagetsi yomwe ili patali ndi r kuchokera pa chaji imodzi ndi iyi:

Kufotokozera: E = munda wamagetsi, k = chosasintha cha Coulomb (9 × 10⁹ Nm²/C²), Q = chaji yamagetsi, r = mtunda kuchokera pa chaji yamagetsi

Iyi ndi njira yamagetsi yopangidwa ndi chaji yamagetsiFomula iyi ingapezeke pogwiritsa ntchito Lamulo la Coulomb.

Minda yamagetsi mkati ndi kunja kwake ndi malo olimba olumikizidwa ndi magetsi ofanana

Chipilala cholimba chokhala ndi mphamvu yamagetsi yofanana kapena yofanana chimakhala ndi mphamvu yonse Q, voliyumu V = 4/3 π R³ ndipo kuchuluka kwa mphamvu mu bwalo lolimba ndi ρ = ​​Q/V. Dziwani mphamvu yamagetsi mphamvu yamagetsi mkati mwa mpira ndi kunja kwa mpira.

a) Malo amagetsi mkati mwa mpira wolimba

Chipilala cholimba chili ndi radius R, pomwe pamwamba pa Gaussian pali chipilala cha radius r, pomwe r < R. Voliyumu ya chipilala cholimba ndi V ndipo voliyumu ya chipilala cha Gaussian ndi V'.

Mphamvu yamagetsi mkati mwa Gauss sphere ndi:

Mphamvu yamagetsi yochokera pakati pa mpira imalowa molunjika pamwamba pa mpira kotero kuti njira yoyendetsera magetsi ndi Φ = E A. Lamulo lachidule la Gauss ndi Φ = Q / ε_o

Munda wamagetsi womwe uli patali ndi r kuchokera pakati pa bwalo lolimba ndi:

Kutengera ndi fomula yomwe ili pamwambapa, gawo lamagetsi (E) limagwirizana ndi mphamvu yamagetsi (Q) ndi utali wa pamwamba pa Gaussian (r), motsatizana ndi kyubiki ya utali wa dera lolimba (R).³).

b) Malo amagetsi kunja kwa bwalo lolimba

Chipilala cholimba chili ndi radius R pomwe pamwamba pa Gaussian pali radius r, pomwe r > R. Mphamvu ya chipilala cholimba ndi Q; chipilala cholimba chili mkati mwa chipilala cha Gaussian kotero mphamvu yamagetsi mkati mwa chipilala cha Gaussian ndi Q.

Mphamvu yamagetsi imatuluka pakati pa mpira ndipo imalowa molunjika pamwamba pa mpira kotero njira yoyendetsera magetsi ndi Φ = E A. Lamulo lachidule la Gauss ndi Φ = Q / ε_o

Munda wamagetsi womwe uli patali r kuchokera pakati pa bwalo lolimba ndi:

Mphamvu yamagetsi mkati ndi kunja kwa chipolopolo cha bwalo lopanda kanthu lokhala ndi magetsi lofanana

Bwalo lopanda kanthu lokhala ndi radius R ndi voliyumu V = 4/3 π R³, ili ndi mphamvu yamagetsi yofanana pakhungu lake yokhala ndi mphamvu yonse QDziwani mphamvu yamagetsi mkati ndi kunja kwa chipolopolo chozungulira.

a) Malo amagetsi mkati mwa bwalo lopanda kanthu

Choncho, dera lopanda kanthu limadziwika ndi mphamvu yamagetsi pamwamba pa dera lopanda kanthu, pomwe palibe mphamvu yamagetsi mkati mwa dera lopanda kanthu. Ngati pamwamba pa Gaussian yomwe yasankhidwa ndi yozungulira ndipo dera la Gaussian lili mkati mwa dera lopanda kanthu, ndiye kuti palibe mphamvu yamagetsi mkati mwa dera la Gaussian. Mphamvu yamagetsi ndi zero, kotero dera lamagetsi nalonso ndi zero. Chifukwa chake, dera lamagetsi mkati mwa dera lopanda kanthu ndi zero.

b) Malo amagetsi kunja kwa bwalo lopanda kanthu

Chipilala chopanda kanthu chili ndi radius R, pomwe pamwamba pa Gaussian pali chipilala chokhala ndi radius r, pomwe r > R.

Mphamvu yamagetsi yochokera pakati pa mpira imalowa molunjika pamwamba pa mpira kotero kuti njira yoyendetsera magetsi ndi Φ = EA = E 4π r²Fomula ya lamulo la Gauss ndi Φ = Q / ε_o .

Munda wamagetsi womwe uli patali ndi r kuchokera pakati pa bwalo lopanda kanthu ndi:

Malo amagetsi pafupi ndi waya woonda wodzaza ndi magetsi

Waya woonda wautali wopanda malire umakhala ndi chaji yamagetsi yofanana yokhala ndi kuchuluka kwa chaji ya λMphamvu yamagetsi pa waya ndi Q = λl. Dziwani mphamvu yamagetsi. mphamvu yamagetsi yozungulira waya woonda.

Pamwamba pa Gaussian pasankhidwa kukhala wozungulira wokhala ndi kutalika kwa l ndi radius r. Pali mitundu iwiri ya pamwamba, yomwe ndi yozungulira yokhala ndi radius r yomwe ili kumapeto onse a silinda (malo a pamwamba ndi .r²) ndi pamwamba pa cylindrical ndi kutalika kwa l (malo ake ndi 2πr l).

Mphamvu yamagetsi ndi yabwino, motero mphamvu yamagetsi imatuluka mu waya molunjika pamwamba pa chubu kotero kuti mphamvu yamagetsi imakhala ndi phindu. Φ = EA = E 2πr lKumbali ina, mphamvu yamagetsi imafanana ndi malekezero onse awiri a chubu chozungulira kotero kuti mphamvu yamagetsi imakhala zero.

Mphamvu yamagetsi yomwe ili patali ndi waya ndi iyi: