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I am wondering if the physical shape of a current carrying conductor will have any effect on the shape of its magnetic field or is it that the magnetic field surrounding any current carrying conductor will always be perfectly round.

For example, let's say that current is passed down a long L-shaped metal bracket, such as the one shown in the drawing below. Will the magnetic field follow the path drawn around the L-bracket, or instead will the magnetic field be perfectly round and will encompass the entire L-shaped bracket?

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Does the physical shape of a current carrying conductor affect the shape of its magnetic field?

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Yes, according to Ampere's law $$\nabla\times\mathbf{B} =\mu_0 \mathbf{J}$$ the shape of the current ($\mathbf{J}$) affects the shape of the magnetic field ($\mathbf{B}$).

Near the L-shaped conductor the magnetic field will follow the L-shape.
Far away from it the magnetic field will be nearly circular.

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