Parallel plates and electric fields

Question

a shark is able to detect electric fields as small as 1.0 μV/m.. Suppose you have a parallel plate capacitor attached to a 1.5 V battery. how far apart must the parallel plates be in order to have an electric field of 1.0 μV/m?

Answer 1

I get 1500km (1.5 × 10^6 m).

Short way:

Using E = V/d -->  d = V/E = 1.5V / 1μV/m = ...

Long way:

{using the following formulas: q=C*V, C=(ε0*A)/d, q=ε0*E*A}

q = C*V  -->  C = q/V

C = (ε0*A)/d  -->  A = (C*d)/ε0 = [(q/V)*d]/ε0 = (q*d)/(V*ε0)

q = ε0*E*A = ε0 * E * [(q*d)/(V*ε0)] = (E * q * d) / V

{q's cancel}

V = E * d  -->  d = V/E = ...