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 5.30 V. Calculate the time required (in s) for the magnetic field to decrease to zero from its maximum value.

Answer 1

Answer:

The time required for the magnetic field to decrease to zero from its maximum value is $1.24 \times 10^{-6}$ sec.

Explanation:

Given :

Magnetic field $B = 1.5 \times 10^{-3} T$

No. of turns $N = 16$

Area of loop $A = 2.75 \times 10^{-4} m^{2}$

Average emf  $=5.3 V$

From the faraday's electromagnetic induction principle,

Average emf $= -N \frac{\Delta \phi}{\Delta t}$

Where $\Delta \phi =$ change in magnetic flux, $\Delta t =$ change in time.

The magnetic flux is given by,

  $\Delta \phi = BA$

In our example, we have to find time required to decrease magnetic field so our above equation is modified as,

 $\Delta \phi = -BA$

$(-)$ for decrease in magnetic field.

  $\Delta t = \frac{NBA}{5.30}$

Where $\Delta t =$ time required for the magnetic field to decrease to zero from its maximum value

  $\Delta t = \frac{1.5 \times 10^{-3} \times 2.75 \times 10^{-4}\times 16 }{5.30}$

       $= 1.24 \times 10^{-6}$ sec.