# How many turns of wire must a coil have in order to induce a voltage of 10.5 volts when exposed to a changing magnetic flux with a rate of 0.0075 Wb/s?

The Faraday's law of electromagnetic induction (incorporating Len's law) gives the induced emf for a coil with $N$ number of turns as:
$\setminus {\xi}_{\text{i"nd}=-N(d\Phi_B)/(dt) \qquad => \qquad | \xi_{"i} n d} | = N | \frac{d \setminus {\Phi}_{B}}{\mathrm{dt}} |$.
| \xi_{"i"nd} | = 10.5 V; \qquad (d\Phi_B)/(dt) = 7.5\times10^{-3} Wb.s^{-1}; \qquad N=?
$N = \frac{| \setminus {\xi}_{\text{i} n d} |}{| \frac{d \setminus {\Phi}_{B}}{\mathrm{dt}} |} = \frac{10.5 V}{7.5 \setminus \times {10}^{- 3} W b . {s}^{- 1}} = 1400$ turns.