Question

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.

Answer 1

Answer:

$1.2*10^{-6}s$

Explanation:

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

$\epsilon = NA \frac{dB}{dt}$

Where

$\epsilon =$ 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

$dt = NA \frac{dB}{\epsilon}$

$t = (16)(2.75*10^{-4})\frac{1.50*10^{-3}}{5.50}$

$t = 1.2*10^{-6}s$

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