What is the magnetic vector potential

Magnetic vector potential, A, is the vector quantity in classical electromagnetism defined so that its curl is equal to the magnetic field: {\textstyle \nabla \times \mathbf {A} =\mathbf {B} \, }. Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well.

Explanation:

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the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.