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Inductive charging is used to wirelessly charge electronic devices ranging from toothbrushes to cell phones. Suppose the base unit of an inductive charger produces a 1.50 ✕ 10−3 T magnetic field. Varying this magnetic field magnitude changes the flux through a 16.0-turn circular loop in the device, creating an emf that charges its battery. Suppose the loop area is 2.75 ✕ 10−4 m2 and the induced emf has an average magnitude of 5.50 V. Calculate the time required (in s) for the magnetic field to decrease to zero from its maximum value.

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Answer:

[tex]1.2*10^{-6}s[/tex]

Explanation:

The problem must be addressed through the concepts of electromotive force. By Faraday's law it is defined that

[tex]\epsilon = NA \frac{dB}{dt}[/tex]

Where

[tex]\epsilon =[/tex] Electromotive Force

N = Number of Loops

A = Area

B = Magnetic Field (chaging through the time)

From this equation and our values, we need to find the time, then we re-arrange the equation

[tex]dt = NA \frac{dB}{\epsilon}[/tex]

[tex]t = (16)(2.75*10^{-4})\frac{1.50*10^{-3}}{5.50}[/tex]

[tex]t = 1.2*10^{-6}s[/tex]

Therefore the time required for the magnetic field to decrease to zero from its maximum value is [tex]1.2*10^{-6}s[/tex]

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