Science Homework Help

We can construct a model of how an electric toothbrush charges as one coil wrapped around another. Coil 1, which is inside of the charger, has a cross-sectional area of 1.6cm2and makes 25 turns in a 0.50cm segment. Coil 2, which is inside the toothbrush, has 34 turns and is wrapped around Coil 1 as shown in Figure 1.1.a.

1. What is the mutual inductance M of the two coils? Assume that Coil 1is an idealized solenoid. (Note: due to some simplifications, your calculated answer will be quite small compared to the actual M for an electric toothbrush).

2. Why is it preferable to construct a toothbrush charger using mutual inductance as opposed to the type of charger where you plug in a device to complete a circuit (e.g., a typical phone charger)? Explain your reasoning.