The Wireless Charging Coil · AI Generator #GEN-434568C4

Physics · electromagnetism

Problem

A smartphone wireless charging pad contains a circular coil with

N = 20

turns and radius

R = 5.0\;\text{cm}

. The coil is placed horizontally and carries an alternating current

I(t) = I_0 \sin(\omega t)

where

I_0 = 0.50\;\text{A}

and

\omega = 2\pi \times 100\;\text{kHz}

. The smartphone contains a single-turn rectangular pickup coil with dimensions

4.0\;\text{cm} \times 6.0\;\text{cm}

placed parallel to and directly above the charging coil at a height where the magnetic field can be considered uniform across the pickup coil. At this height, the magnetic field produced by the charging coil has magnitude

B = 1.2 \times 10^{-4}\;\text{T}

. Find the maximum induced EMF in the smartphone's pickup coil.

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