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 1.10 ✕ 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 3.75 ✕ 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. Apply Faraday's law.

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Faraday's first law of electromagnetic induction states, “Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced.

emf = NdФ/dt

emf = NBA/t

where;

N is number of turns of the coil
A is area of the coil
B is magnetic field
t is time

The time required (in s) for the magnetic field to decrease to zero from its maximum value is calculated as follows;

t = NBA/emf

t = (16 x 1.1 x 10⁻³ x 3.75 x 10⁻⁴) / (5.5)

t = 1.2 x 10⁻⁶ s

Thus, the time required (in s) for the magnetic field to decrease to zero from its maximum value is 1.2 x 10⁻⁶ s.

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