# Electromagnetic Fields in Wireless Power Transmission

Electromagnetic Fields in Wireless Power Transmission

Wireless power transmission makes use of a pair of magnetically coupled coils, each in series with a capacitor. The characteristic frequency is discussed in the companion Demonstration "Wireless Power Transmission." The present Demonstration is concerned with the electromagnetic fields associated with a wireless transmission system. The parameters are the following (as defined in the companion Demonstration):

V

i

V

rms

r

i

r

o

C

1

C

2

L

1

L

2

L

12

a=b=0.5m

R=5mm

N

1

N

2

d=1m

Maximum power is transmitted at the resonance frequency =87.5kHz.

f

res

The instantaneous input voltage (t) and currents (t), (t) can be defined from the corresponding phaser solution of the circuit equation. The field of the coaxial coil system can be readily analyzed using the vector potential , which is a linear function of (t) and (t). Assuming a near field, the electric and magnetic fields can be obtained by and , respectively. The power flow through space is given by the Poynting vector .

v

i

i

1

i

2

A

i

1

i

2

E=-∂A/∂t

H=curlA/

μ

0

S=EH

The field in the - plane is shown for a selected frequency and phase (i.e., time). The electric field perpendicular to the - plane is not shown. The magnetic field and Poynting vectors are shown by blue and orange arrows, respectively. The color indicates the magnitude of the energy density . All of these are plotted on a logarithmic scale.

x

z

x

z

w=/2+/2

ϵ

0

2

E

μ

0

2

H