- #1

millo

- 2

- 2

- Homework Statement:
- My question is how do we know that faraday's law right side is required for all surfaces.

- Relevant Equations:
- ∫_c Edl =-d/dt ∫_s Bda

∫

_{c}Edl =-d/dt∫_{s}BdaYou are using an out of date browser. It may not display this or other websites correctly.

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- Thread starter millo
- Start date

- #1

millo

- 2

- 2

- Homework Statement:
- My question is how do we know that faraday's law right side is required for all surfaces.

- Relevant Equations:
- ∫_c Edl =-d/dt ∫_s Bda

∫_{c} Edl =-d/dt∫_{s}Bda

- #2

- 5,695

- 2,473

Since ##\nabla\cdot \vec{B}=0## (Gauss's law for magnetism) we can set ##\vec{B}=\nabla\times\vec{A}##. Stokes theorem tell us that $$\iint_S \vec{B}\cdot d\vec{S}=\iint _S(\nabla\times \vec{A})\cdot d\vec{S}=\oint_C\vec{A}\cdot d\vec{l}$$ so the surface integral of B over S will equal the line integral of A over the curve C, thus it remains constant for all surfaces S with the same boundary C.

- #3

millo

- 2

- 2

Yes this is what I meat, thanks for answer.

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