Question

The peak magnetic field strength in a residential microwave oven is$\mathbf{9}\mathbf{.}\mathbf{20}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}}\mathbf{T}$ . (a) What is the intensity of the microwave? (b) What is unreasonable about this result? (c) What is wrong about the premise?

Short answer

a. The intensity of the microwave is$1.01\times {10}^8\mathrm{W}/{\mathrm{m}}^2$ .

b. The intensity of the microwave is too high that cannot be possible.

c. The assumption about the magnetic field strength is inconsistent.

Step-by-step solution

Definition of Concept

Intensity: The power transferred per unit area is the intensity of radiant energy in physics, where the area is measured on a plane perpendicular to the energy's propagation direction.

Find the intensity of the microwave

(a)

Considering the given information,

Peak magnetic field strength,${\mathrm{B}}_0=9.20\times {10}^{-5}\mathrm{T}$

Apply the formula,

The microwave's intensity is expressed as follows:

$\mathrm{I}=\frac{{\mathrm{cB}}_0^2}{2{\mathrm{\mu }}_0}$………………..(1)

Here, I denote microwave intensity, the maximum magnetic field ${\mathrm{B}}_0$, and${\mathrm{\mu }}_0$ represents the permeability of free space.

Substitute, $\mathrm{\mu }=4\mathrm{\pi }\times {10}^{-7}\mathrm{T}·\mathrm{m}/\mathrm{A}$, $\mathrm{c}=3\times {10}^8\mathrm{m}/\mathrm{s}$ and ${\mathrm{B}}_0=9.20\times {10}^{-5}\mathrm{T}$ in the above expression, we get

$$\begin{gathered} \mathrm{I}=\frac{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right){\left(9.20\times {10}^{-5}\mathrm{T}\right)}^2}{2\left(4\mathrm{\pi }\times {10}^{-7}\mathrm{T}·\mathrm{m}/\mathrm{A}\right)} \\ =1.01\times {10}^6\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

Therefore, the required intensity of the microwave is $1.01\times {10}^6\mathrm{W}/{\mathrm{m}}^2$.

Find the unreasonable about this result

(b)

The microwave's calculated intensity is too high, and this value of intensity is excessive

for a microwave oven. As a result, the microwave oven's intensity is excessive.

Therefore, the intensity of the microwave is too high which cannot be possible.

Find the wrong about the premise

(c)

The specified magnetic field strength number is far too high for a microwave to handle.

As a result, the magnetic field strength assumption is unreliable.

Therefore, the assumption about the magnetic field strength is inconsistent.