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

The time required for the magnetic field to decrease to zero from its maximum value is
`1.24 * 10^(-6)` sec.

Step-by-step explanation:

Given :

Magnetic field
`B = 1.5 * 10^(-3) T`

No. of turns
`N = 16`

Area of loop
`A = 2.75 * 10^(-4) m^(2)`

Average emf
`=5.3 V`

From the faraday's electromagnetic induction principle,

Average emf
`= -N (\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 = (NBA)/(5.30)`

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

`\Delta t = (1.5 * 10^(-3) * 2.75 * 10^(-4)* 16 )/(5.30)`

`= 1.24 * 10^(-6)` sec.