The inductance \( L \) of a coil can be calculated using Faraday's law of electromagnetic induction, which relates the induced electromotive force (emf) in a coil to the rate of change of current. The formula is given by:
\[ \text{emf} = -L \frac{di}{dt} \]
where:
- \( \text{emf} \) is the induced electromotive force in volts (V),
- \( L \) is the inductance in henries (H),
- \( \frac{di}{dt} \) is the rate of change of current in amperes per second (A/s).
Rearranging this equation to solve for inductance \( L \), we have:
\[ L = -\frac{\text{emf}}{\frac{di}{dt}} \]
In this case, the emf is given as 6.6 V and the rate of change of current \( \frac{di}{dt} \) is given as 10 A/s. Substituting these values into the equation:
\[ L = -\frac{6.6}{10} \]
Calculating this gives:
\[ L = -0.66 , \text{H} \]
The negative sign indicates that the direction of the induced emf opposes the change in current (according to Lenz's law), but the magnitude of the inductance is typically reported as a positive value. Therefore, the inductance of the coil is:
\[ L = 0.66 , \text{H} \]