Answer to Question #268141 in Electricity and Magnetism for Qwerty

Question

The electric field and the magnetic field in free space are given by

E=\frac{50}{\rho}\cos(10^{6}t+\beta z)a_{\phi} V/mE=

ρ

50

​

cos(10

6

t+βz)a

ϕ

​

V/m

H=\frac{H_{o}}{\rho}\cos(10^{6}t+\beta z)a_{\rho} A/mH=

ρ

H

o

​

​

cos(10

6

t+βz)a

ρ

​

A/m

Express these in phasor form and determine the constants H_{o}H

o

​

and \betaβ such that the fields satisfy Maxwell’s equations.

Answer 1

$E=\frac{50}{\rho}\cos(10^{6}t+\beta z)a_{\phi} \frac Vm,$

$H=\frac{H_o}{\rho}\cos(10^{6}t+\beta z)a_{\rho}~ \frac Am,$

$H_o=50,~\beta=1.$