Answer
238.
Work Step by Step
Equate 2 expressions for L, $\frac{\epsilon}{|di/dt|}$ and $\frac{N\Phi_B}{i}$.
Solve for N, the number of turns.
$$N =\frac{\epsilon i}{\Phi_B |di/dt|} =\frac{(0.0126V)(1.40A)}{(0.00285Wb)(0.0260A/s)}=238$$
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