Question

Many athletes and cool tech lovers wear a smartwatch. like the Apple Watch, to monitor their fitness and sleep patterns, receive emails, and make phone calls. The watch has an internal battery that is charged wirelessty by induction. The watch is placed faceup onto a charging base (see the photo). There is a charging coil (the primary) in the base and a receiving coil (the secondary) just inside the back faceplate of the watch. An alternating current is sent through the base coil, which creates a changing magnetic field. This produces a change in magnetic flux through the watch's coil, which induces an emf in that coil, thereby charging the watch's battery. Assume the secondary coil has 10 turns with an average area of 1.77 cm ², If the emf induced in the coil is 3.80 V, what is the rate of change of the magnetic field within the charging coil? Consider again the hearing aid ecuipped with the T-colt as described in Exarnple 10. When the loap system in the room is initially turned on. a sunge of current around the loop induces an ersf in the T-col of 7.2×10 ⁵V What is the value of the peak magnetic field in the room, if it is reached after 65 ms ? Number=_______units

Answer 1

Charging the Apple Watch and certain hearing aids both involve electromagnetic induction, fundamental physics principle. The rate of change of the magnetic field in the watch's charging coil can be calculated using Faraday's law of electromagnetic induction, where a rearranged version of ΔΦ = -n * ΔB * A can be used to find ΔB. The magnetic field in the hearing aid situation can also be computed using this law.

Step-by-step explanation:

Many athletes and tech enthusiasts use a smartwatch like the Apple Watch to monitor various aspects of their lifestyle, including their sleep and fitness patterns. The watch is most commonly charged using wireless induction, which relies on the principles of electromagnetic induction.

To calculate the rate of change of the magnetic field within the charging coil, we can use Faraday's law of electromagnetic induction. The law is given by the formula ΔΦ = -n * ΔB * A, where ΔΦ is the change in magnetic flux, n is the number of turns in the coil, ΔB is the change in magnetic field and A is the area. We can rearrange the formula to solve for ΔB: ΔB = ΔΦ / (n * A).

Given the values in the question (n = 10, A = 1.77 cm² and emf = 3.80 V), we can calculate ΔB. Please remember to convert the area from cm² to m² (1 cm² = 0.0001 m²) for consistency in units.

The second part of the question involves a hearing aid equipped with a T-coil. The calculation of the magnetic field (B) involves similar steps as described above, but with a need to consider the duration of the surge as well.

Learn more about Electromagnetic Induction