Question

Microwaves in a home microwave oven can be modeled as a linearly polarized plane wave in vacuum with a magnetic field given by  B⃗ =B0sin(ky+ωt)x^B→=B0sin⁡(ky+ωt)x^. Here, B0=B0= 0.22 mT and  ω=ω= 2 ×1010×1010 rad/sec.

1)

What is the wavelength?

λ=λ= 9.42 cm

λ=λ= 1.88 × 10¹⁷ cm

λ=λ= 1.5 cm

2)

The associated electric field is given by:

E⃗ =−B0csin(ky+ωt)z^E→=−B0csin⁡(ky+ωt)z^

E⃗ =−B0csin(ky−ωt)z^E→=−B0csin⁡(ky−ωt)z^

E⃗ =−B0csin(ky+ωt)y^E→=−B0csin⁡(ky+ωt)y^

E⃗ =B0csin(ky−ωt)y^E→=B0csin⁡(ky−ωt)y^

E⃗ =B0csin(ky+ωt)z^E→=B0csin⁡(ky+ωt)z^

3)

A round dinner plate of radius r = 8 cm is placed in the microwave oven in an orientation perpendicular to the direction of propagation, as shown. Find the average power the plate can absorb. (Assume the plate area is smaller than the wave itself, and the plate absorbs all the energy impinging on it).

〈P〉=〈P〉= 1.16 × 10⁵ W

〈P〉=〈P〉= 1.29 × 10^-12 W

〈P〉=〈P〉= 5.78 × 10⁶ W

〈P〉=〈P〉= 6.42 × 10^-11 W

〈P〉=〈P〉= 91200 W

Answer 1

use the angular frequency to find the linear frequency and use that to find the wavelength using the speed of light. Use properties of electromagnetic wave to find the equation of electric field as shown below