(a) Define scalar potential. Prove that, in any simply connected region, F =-V@ where p is a scalar function. (b) Derive a relation for Vx B in curvilinear coordinates, where B is a vector in...

Do and b just firstly

Extracted text: (a) Define scalar potential. Prove that, in any simply connected region, F =-V@ where p is a scalar function. (b) Derive a relation for Vx B in curvilinear coordinates, where B is a vector in curvilinear coordinates. (a) Explain the terms covariant and contra-variant derivatives. (b) Prove that, in the case of spherical polar coordinates, the product of Jacobian and its inverse is unity.