Question

Some electronic devices such as phones and watches can be charged wirelessly. In the charger, there is a coil that generates a rapidly changing magnetic field. In the device, there is a second, 100-turn rectangular coil with side length of 3.0 cm and 4.0 cm. If the maximum rate of the change of the magnetic field and the second coil is 53 T/s, what is the EMF induced in this coil?

Answer 1

For a rectangle the area will be

$$ \begin{aligned} A &=(3.0 \mathrm{~cm})(4.0 \mathrm{~cm}) \\ &=12.0 \mathrm{~cm}^{2} \\ &=12.0 \times 10^{-4} \mathrm{~m}^{2} \end{aligned} $$

The induced emf in the coil is,

$$ \begin{aligned} \varepsilon &=-N \frac{d \phi_{B}}{d t} \\ &=-N A \frac{d B}{d t} \\ &=-(100)\left(12.0 \times 10^{-4} \mathrm{~m}^{2}\right)(53 \mathrm{~T} / \mathrm{s}) \\ &=-6.36 \mathrm{~V} \end{aligned} $$

The magnitude of induced emf is \(|\varepsilon|=6.36 \mathrm{~V}\)