problem 22.23
the magnetic field in a em wave traveling in free space has an rms strength of 24.1 nt
part a
how long does it take to deliver 385 j of energy to 1.05 cm² of a wall that it hits perpendicularly?
express your answer using three significant figures.
δt =

Question

Accepted Answer

# Explanation:
## Step1: Calculate the intensity $I$
The formula for the intensity of an electromagnetic wave is $I = \frac{cB_{rms}^{2}}{\mu_{0}}$, where $c = 3\times10^{8}\ m/s$, $B_{rms}=24.1\times10^{-9}\ T$, and $\mu_{0} = 4\pi\times 10^{-7}\ T\cdot m/A$.
$$
\begin{align*}
I&=\frac{(3\times 10^{8}\ m/s)(24.1\times 10^{-9}\ T)^{2}}{4\pi\times 10^{-7}\ T\cdot m/A}\
&=\frac{(3\times 10^{8})(24.1^{2}\times 10^{-18})}{4\pi\times 10^{-7}}\
&=\frac{(3\times 10^{8})(580.81\times 10^{-18})}{4\pi\times 10^{-7}}\
&=\frac{1.74243\times 10^{-7}}{4\pi\times 10^{-7}}\
&=\frac{1.74243}{4\pi}\
&\approx0.139\ W/m^{2}
\end{align*}
$$
## Step2: Convert the area $A$ to $m^{2}$
Given $A = 1.05\ cm^{2}=1.05\times 10^{-4}\ m^{2}$
## Step3: Use the formula $U = IAt$ to solve for $t$
Rearrange $t=\frac{U}{IA}$, where $U = 385\ J$, $I\approx0.139\ W/m^{2}$, $A = 1.05\times 10^{-4}\ m^{2}$
$$
\begin{align*}
t&=\frac{385\ J}{(0.139\ W/m^{2})(1.05\times 10^{-4}\ m^{2})}\
&=\frac{385}{0.139\times1.05\times 10^{-4}}\
&=\frac{385}{1.4595\times 10^{-5}}\
&\approx2.64\times 10^{7}\ s
\end{align*}
$$

# Answer:
$\Delta t = 2.64\times 10^{7}\ s$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Calculate the intensity \(I\)

Step2: Convert the area \(A\) to \(m^{2}\)

Step3: Use the formula \(U = IAt\) to solve for \(t\)

Answer: