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can someone please tell me what the exact meaning of "A" in the formula for finding magnetic flux stands for?
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A represents the area you're looking at. For example, if you have a square wire whose side length is 1 meter, then the area it covers is 1 square meter.
area through which magnetic field lines pass perpendicularly
Depends on which form. If we have: \[ \Phi=\oint_{\partial \Sigma}A\cdot dw \]Then it is the vector potential through that surface component. Otherwise, if we have: \[ \Phi= B\cdot \vec{A} \]Then it's the area vector which points outwards-normal to the surface and \(|A|\) is the area of the surface.
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