Elektrický potenciál
φ
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4
π
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\varphi = \frac{1}{4 \pi \varepsilon_0} \int_V \frac{\rho{\left(\vec r'\right)}}{{\left\lvert \vec r - \vec r'\right\rvert}} {\mathrm dV}
φ
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1
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V
E
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3
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E = \frac{1}{4 \pi \varepsilon_0} \int_S \frac{\sigma{\left(\vec r'\right)}}{{\left\lvert \vec r - \vec r'\right\rvert}^3} {\left(\vec r - \vec r'\right)} \,{\mathrm dS}
E
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4
π
ε
0
1
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3
σ
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d
S
Substituce
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⋅
∣
J
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d
v
d
w
\int_V f{\left(x,y,z\right)} \,{\mathrm dx} \,{\mathrm dy} \,{\mathrm dz} = \int_V f{\left(x{\left(u,v,w\right)}, y{\left(u,v,w\right)}, z{\left(u,v,w\right)}\right)} \cdot {\left\lvert J\right\rvert} \,{\mathrm du} \,{\mathrm dv} \,{\mathrm dw}
∫
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⋅
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J
∣
d
u
d
v
d
w
∫
l
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l
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⋅
∣
Φ
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t
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d
t
\int_l f{\left(x,y,z\right)} \,{\mathrm dl} = \int_l f{\left(x{\left(t\right)}, y{\left(t\right)}, z{\left(t\right)}\right)} \cdot {\left\lvert \dot{\vec \Phi}{\left(t\right)}\right\rvert} \,{\mathrm dt}
∫
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Φ
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d
t
∫
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F
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\int_l \vec F{\left(x,y,z\right)} \,{\mathrm dl} = \int_l \vec F{\left(x{\left(t\right)}, y{\left(t\right)}, z{\left(t\right)}\right)} \cdot \dot{\vec \Phi}{\left(t\right)} \,{\mathrm dt}
∫
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Φ
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