Question

The transmitter coil shown in Figure 1 is designed for wireless power transfer in small electronic devices. It comprises a coil wound with a round copper wire of diameter d = 4mm, wound in a planar spiral with N=5 turns, an inner radius r, in meters, and a radial pitch p=1 meter. The coil is excited at variable frequency by a circulating current of amplitude IA.

(a) Theoretical Calculation and Verification

Using the expression for the inductance of a circular coil developed in the class (1), estimate the inductance L = 2πμN²l/ln(r2/r1), where r1 and r2 are the inner and outer radii, μ is the permeability, and l is the coil length.
Open the model of the coil provided in Learning Central and run it for a range of IA values.
Use a coil line along the coil axis to verify the resulting magnetic flux density.
Account for any differences between the theoretical and numerical findings

Answer 1

The inductance of the transmitter coil for wireless power transfer is calculated using a provided formula and numerical simulation is used for verification. discrepancies may be due to assumptions in the model or the precision of the simulation.

Step-by-step explanation:

The question relates to the calculation of the inductance L of a transmitter coil designed for wireless power transfer in small electronic devices. Using the provided equation L = 2πμN²l/ln(r2/r1), we can estimate L by substituting the given values such as the inner and outer radii (r1 and r2), the number of turns N, coil length l, and the permeability μ. verification using simulation involves running a digital model of the coil for a range of current amplitudes IA and using a coil line along the coil axis to observe the magnetic flux density. Discrepancies between the theoretical and numerical findings could be attributed to factors such as the assumptions made in the theoretical model, precision of numerical simulations, or real-world constraints not accounted for in the model.

As an example for similar calculations, a 200-turn flat coil with a radius of 15 cm and subjected to a magnetic field of 1.00×10⁻¹² T could be used to estimate incident power, induced emf, and other related electrical properties.