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samenvatting fysica miv wiskunde: potentiaal
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Samenvatting van de powerpoints van dit hoofdstuk voor het vak fysica miv wiskunde
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Fysica miv wiskunde: fysica – POTENTIAALElektrische potentiële energie
1 Q
Elektrisch veld in punt P: ⃗
E = . ⃗ e
4 π ε0 r2 r
Kracht op lading q in punt P: ⃗
F =q E⃗ = 1 . qQ ⃗ e F =−⃗
⃗ ∇U
4 π ε0 r2 r
1 qQ
Potentiële energie van q: U = .
4 π ε0 r
o Op een afstand oneindig is deze 0
o Arbeid die nodig is om lading q van oneindig naar P te brengen
Verschil in potentiële energie tussen P en P0
P P
o ∆ U = -W = -∫ ⃗
F . d ⃗L = -q∫ ⃗
E . d ⃗L
P0 P0
⃗
F is centraal en dus conservatief, de arbeid is onafhankelijk van de gevolgede weg.
Als je twee positieve ladingen naar elkaar duwt moet je heen heel veel arbeid
leveren, maar om terug te gaan is er geen arbeid nodig.
∮⃗ E.d ⃗
L=0
Potentiaal
Potentiaal en spanning
Potentiaal V = potentiële energie/eenheid van lading
U Q
V= = (volt - V)
q 4 π ε0 r
Spanning ∆ V: potentiaalverschil tussen twee punten
P
∆ V = V1 – V0 = -∫ ⃗
E . d ⃗L
P0
Potentiaal rond puntlading
Q
V=
4 π ε0 r
voor een oneindige afstand, is de potentiaal 0
Want: potentiaal in een punt is de arbeid die nodig is om een positieve lading van oneindig
naar dat punt te brengen.
Potentiaal rond continue of discrete ladingsverdelingen
1 dQ 1 Qi
Continu: V =
4 π ε0
∫ r
discreet: V = ∑
4 π ε0 i ri
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