I'm not really sure what I'm being asked to do with the following questions. Will someone help me? How can you show that E(r)=-gradV(r) has zero curl an is irrotational, i.e. the quantity (grad x E) =0 How can you show that the magnetic field ,B(r)=grad x A(r), is divergenceless i.e. that the quantity grad dot B(r) =0?