I believe the answer is c but I’m not 100% sure
Answer:
The magnetic field strength, the energy density, and the power flow per unit area are
,
and 13.18 W/m².
Explanation:
Given that,
Electromagnetic wave strength E= 70.5 V/m
(I). We need to calculate the magnetic field strength
Using formula of Electromagnetic wave strength
![c= \dfrca{E}{B}](https://tex.z-dn.net/?f=c%3D%20%5Cdfrca%7BE%7D%7BB%7D)
![B=\dfrac{E}{c}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7BE%7D%7Bc%7D)
![B=\dfrac{70.5 }{3\times10^{8}}](https://tex.z-dn.net/?f=B%3D%5Cdfrac%7B70.5%20%7D%7B3%5Ctimes10%5E%7B8%7D%7D)
![B=2.35\times10^{-7}\ T](https://tex.z-dn.net/?f=B%3D2.35%5Ctimes10%5E%7B-7%7D%5C%20T)
(II). We need to calculate the energy density
Using formula of energy density
![\mu_{total}=\mu_{E}+\mu_{B}](https://tex.z-dn.net/?f=%5Cmu_%7Btotal%7D%3D%5Cmu_%7BE%7D%2B%5Cmu_%7BB%7D)
![\mu_{total}=\dfrac{1}{2}\epsilon_{0}E^2+\dfrac{1}{2}\dfrac{B^2}{\mu_{0}}](https://tex.z-dn.net/?f=%5Cmu_%7Btotal%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Cepsilon_%7B0%7DE%5E2%2B%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7BB%5E2%7D%7B%5Cmu_%7B0%7D%7D)
![\mu_{total}=\dfrac{1}{2}\times8.85\times10^{-12}\times(70.5)^2+\dfrac{1}{2}\times\dfrac{(2.35\times10^{-7})^2}{4\pi\times10^{-7}}](https://tex.z-dn.net/?f=%5Cmu_%7Btotal%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ctimes8.85%5Ctimes10%5E%7B-12%7D%5Ctimes%2870.5%29%5E2%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%5Cdfrac%7B%282.35%5Ctimes10%5E%7B-7%7D%29%5E2%7D%7B4%5Cpi%5Ctimes10%5E%7B-7%7D%7D)
![\mu_{total}=4.396\times10^{-8}\ J/m^3](https://tex.z-dn.net/?f=%5Cmu_%7Btotal%7D%3D4.396%5Ctimes10%5E%7B-8%7D%5C%20J%2Fm%5E3)
(III). We need to calculate the power flow per unit area
Using formula of poynting vector
![S=\dfrac{1}{\mu_{0}}EB](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7B1%7D%7B%5Cmu_%7B0%7D%7DEB)
Put the value into the formula
![S=\dfrac{1}{4\pi\times10^{-7}}\times70.5\times2.35\times10^{-7}](https://tex.z-dn.net/?f=S%3D%5Cdfrac%7B1%7D%7B4%5Cpi%5Ctimes10%5E%7B-7%7D%7D%5Ctimes70.5%5Ctimes2.35%5Ctimes10%5E%7B-7%7D)
![S=13.18\ W/m^2](https://tex.z-dn.net/?f=S%3D13.18%5C%20W%2Fm%5E2)
Hence, The magnetic field strength, the energy density, and the power flow per unit area are
,
and 13.18 W/m².
Answer:
![d = 0.344 m](https://tex.z-dn.net/?f=d%20%3D%200.344%20m)
Explanation:
mass of the crate = 5 kg
Force on crate = 0.22 N
![acceleration = \frac{Force}{mass}](https://tex.z-dn.net/?f=acceleration%20%3D%20%5Cfrac%7BForce%7D%7Bmass%7D)
![acceleration = \frac{0.22}{5}](https://tex.z-dn.net/?f=acceleration%20%3D%20%5Cfrac%7B0.22%7D%7B5%7D)
![a = 0.044 m/s^2](https://tex.z-dn.net/?f=a%20%3D%200.044%20m%2Fs%5E2)
now the speed of the crate after t = 10 s
![v_f = v_i + at](https://tex.z-dn.net/?f=v_f%20%3D%20v_i%20%2B%20at)
![v_f = 0 + 0.044 \times 10](https://tex.z-dn.net/?f=v_f%20%3D%200%20%2B%200.044%20%5Ctimes%2010)
![v_f = 0.44 m/s](https://tex.z-dn.net/?f=v_f%20%3D%200.44%20m%2Fs)
Now the time taken by the crate to reach the orchestra pit
![y = \frac{1}{2}gt^2](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B2%7Dgt%5E2)
![3 = \frac{1}{2}(9.8)t^2](https://tex.z-dn.net/?f=3%20%3D%20%5Cfrac%7B1%7D%7B2%7D%289.8%29t%5E2)
![t = 0.78 s](https://tex.z-dn.net/?f=t%20%3D%200.78%20s)
now we know that
![d = vt](https://tex.z-dn.net/?f=d%20%3D%20vt)
![d = (0.44)(0.78)](https://tex.z-dn.net/?f=d%20%3D%20%280.44%29%280.78%29)
![d = 0.344 m](https://tex.z-dn.net/?f=d%20%3D%200.344%20m)
In order to determine this, we will first need some conversions. We will need to convert metric tons and grams into one another and also cubic centimeters to cubic meters into one another.
1 metric ton = 1000 kg
1 kg = 1000 grams
1 metric ton = 10⁶ grams
So 10⁶ grams / metric ton
1 meter = 100 cm
1 m³ = (100)³ cm³
1 m³ = 10⁶ cm³
So 10⁶ cm⁶ / m³
Now, we manipulate the given value:
(19.3 grams / cm³) * (1 metric ton / 10⁶ grams) * (10⁶ cm³ / m³)
= 19.3 metric tons / m³
The density of gold is 19.3 metric tons meter meter cubed.
Kinetic and potential energy