seira askhsewn 2 - PMS “FUSIKH KAI TEQNOLOGIKES...

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PMS FUSIKH KAI TEQNOLOGIKES EFARMOGES TOMEAS FUSIKHS SEMFE EMP - SQOLH MHQANOLOGWN MHQANIKWN EMP - EKEFE DHMOKRITOS HLEKTROMAGNHTISMOS I: DEUTERH SEIRA ASKHSEWN 9. 'Enac q¸roc V peribˆlletai apì mia epifˆneia S pou apoteleÐtai apì diˆforec ag¸gimec apifˆneiec S k (mÐa mporeÐ na brÐsketai kai sto ˆpeiro) pou brÐskontai sta antÐstoiqa du- namikˆ V k . Jewr ste th sunˆrthsh Ψ( ~x ) pou sumperifèretai ex upojèsewc omalˆ sto V kai sto S kai orÐste thn posìthta W [Ψ] 1 8 πk Z V d 3 x | ~ Ψ | 2 . ApodeÐxte to akìloujo je¸rhma: Me thn pro ¨ upìjesh ìti h Ψ( ~x ) paÐrnei tic timèc V k stic epifˆneiec S k , to W [Ψ] eÐnai apìluto elˆqisto an kai mìno an h Ψ( ~x ) ikanopoieÐ thn exÐswsh Laplace sto V. 10. ApodeÐxte to akìloujo je¸rhma: An kˆpoioi agwgoÐ brÐskontai se sugkekrimènec jèseic kai fèroun dedomèna fortÐa, h eisagwg  enìc prìsjetou afìrtistou monwmènou agwgoÔ sthn perioq  pou peribˆlletai apì touc agwgoÔc autoÔc qamhl¸nei thn hlektrostatik  enèrgeia. 11. Na lujeÐ h (didiˆstath) exÐswsh tou Laplace gia to eswterikì enìc kulÐndrou me aktÐna R me thn oriak  sunj kh V ( ρ = R,φ,z ) = f ( φ ) . Na apodeiqjeÐ ìti to apotèlesma mporeÐ na grafteÐ me th morf : V ( ρ,φ,z ) = 1 π Z π 0 0 f ( φ
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seira askhsewn 2 - PMS “FUSIKH KAI TEQNOLOGIKES...

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