Question

the gradient of the magnetic vector potential can be expressed ​

Answer 1

Although we cannot express the magnetic field as the gradient of a scalar potential function, we shall define a vector quantity A whose curl is equal to the magnetic field: B=curl A=∇×A.For, if ψ is some scalar quantity, we can always add ∇ψ to A without affecting B, because ∇×∇ψ=curl grad ψ=0.