(a) Confirm that (r) = r E and A = 1/2 r B are acceptable scalar and vector potentials, respectively, for a constant

(a) Confirm that ϕ(r) = −r · E and A = −1/2 r × B are acceptable scalar and vector potentials, respectively, for a constant electric field E and a constant magnetic field B.
(b) By direct computation of B = ∇ × A and E = −∇_ϕ − ∂A/∂t, prove that the generalizations of the formulae in part (a) to arbitrary time-dependent fields are

S (r, 1) = -r. d E(r, t) A(r, 1) = -fdx 0 d r x B(r, t).