<h3><u>Volume is 0.1848 m³</u></h3><h3 />
Explanation:
<h2>Given:</h2>
m = 49.9 kg
ρ = 270 kg/m³
<h2>Required:</h2>
volume
<h2>Equation:</h2>
![ρ \:= \:\frac{m}{v}](https://tex.z-dn.net/?f=%CF%81%20%5C%3A%3D%20%5C%3A%5Cfrac%7Bm%7D%7Bv%7D)
where: ρ - density
m - mass
v - volume
<h2>Solution:</h2>
Substitute the value of ρ and m
![ρ \:= \:\frac{m}{v}](https://tex.z-dn.net/?f=%CF%81%20%5C%3A%3D%20%5C%3A%5Cfrac%7Bm%7D%7Bv%7D)
![270\: kg/m³\:= \:\frac{49.9\:kg}{v}](https://tex.z-dn.net/?f=270%5C%3A%20kg%2Fm%C2%B3%5C%3A%3D%20%5C%3A%5Cfrac%7B49.9%5C%3Akg%7D%7Bv%7D)
![(v)\:270\: kg/m³\:= \:49.9\:kg](https://tex.z-dn.net/?f=%28v%29%5C%3A270%5C%3A%20kg%2Fm%C2%B3%5C%3A%3D%20%5C%3A49.9%5C%3Akg)
![v\:= \:\frac{49.9\:kg}{270\: kg/m³}](https://tex.z-dn.net/?f=v%5C%3A%3D%20%5C%3A%5Cfrac%7B49.9%5C%3Akg%7D%7B270%5C%3A%20kg%2Fm%C2%B3%7D)
![v\:= \:0.1848\:m³](https://tex.z-dn.net/?f=v%5C%3A%3D%20%5C%3A0.1848%5C%3Am%C2%B3)
<h2>Final Answer:</h2><h3><u>Volume is 0.1848 m³</u></h3>
<span>Increase the wavelength of the light
</span>
Answer:
292.3254055 W/m²
469.26267 V/m
![1.56421\times 10^{-6}\ T](https://tex.z-dn.net/?f=1.56421%5Ctimes%2010%5E%7B-6%7D%5C%20T)
Explanation:
P = Power of bulb = 90 W
d = Diameter of bulb = 7 cm
r = Radius = ![\frac{d}{2}=\frac{7}{2}=3.5\ cm](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B2%7D%3D%5Cfrac%7B7%7D%7B2%7D%3D3.5%5C%20cm)
= Permittivity of free space = ![8.85\times 10^{-12}\ F/m](https://tex.z-dn.net/?f=8.85%5Ctimes%2010%5E%7B-12%7D%5C%20F%2Fm)
c = Speed of light = ![3\times 10^8\ m/s](https://tex.z-dn.net/?f=3%5Ctimes%2010%5E8%5C%20m%2Fs)
The intensity is given by
![I=\frac{P}{A}\\\Rightarrow I=\frac{90}{4\pi 0.035^2}\\\Rightarrow I=5846.50811\ W/m^2](https://tex.z-dn.net/?f=I%3D%5Cfrac%7BP%7D%7BA%7D%5C%5C%5CRightarrow%20I%3D%5Cfrac%7B90%7D%7B4%5Cpi%200.035%5E2%7D%5C%5C%5CRightarrow%20I%3D5846.50811%5C%20W%2Fm%5E2)
5% of this energy goes to the visible light so the intensity is
![I=0.05\times 5846.50811\\\Rightarrow I=292.3254055\ W/m^2](https://tex.z-dn.net/?f=I%3D0.05%5Ctimes%205846.50811%5C%5C%5CRightarrow%20I%3D292.3254055%5C%20W%2Fm%5E2)
The visible light intensity at the surface of the bulb is 292.3254055 W/m²
Energy density of the wave is
![u=\frac{1}{2}\epsilon_0E^2](https://tex.z-dn.net/?f=u%3D%5Cfrac%7B1%7D%7B2%7D%5Cepsilon_0E%5E2)
Energy density is also given by
![\frac{I}{c}=\frac{1}{2}\epsilon_0E^2\\\Rightarrow E=\sqrt{\frac{2I}{c\epsilon_0}}\\\Rightarrow E=\sqrt{\frac{2\times 292.3254055}{3\times 10^8\times 8.85\times 10^{-12}}}\\\Rightarrow E=469.26267\ V/m](https://tex.z-dn.net/?f=%5Cfrac%7BI%7D%7Bc%7D%3D%5Cfrac%7B1%7D%7B2%7D%5Cepsilon_0E%5E2%5C%5C%5CRightarrow%20E%3D%5Csqrt%7B%5Cfrac%7B2I%7D%7Bc%5Cepsilon_0%7D%7D%5C%5C%5CRightarrow%20E%3D%5Csqrt%7B%5Cfrac%7B2%5Ctimes%20292.3254055%7D%7B3%5Ctimes%2010%5E8%5Ctimes%208.85%5Ctimes%2010%5E%7B-12%7D%7D%7D%5C%5C%5CRightarrow%20E%3D469.26267%5C%20V%2Fm)
The amplitude of the electric field at this surface is 469.26267 V/m
Amplitude of a magnetic field is given by
![B=\frac{E}{c}\\\Rightarrow B=\frac{469.26267}{3\times 10^8}\\\Rightarrow B=1.56421\times 10^{-6}\ T](https://tex.z-dn.net/?f=B%3D%5Cfrac%7BE%7D%7Bc%7D%5C%5C%5CRightarrow%20B%3D%5Cfrac%7B469.26267%7D%7B3%5Ctimes%2010%5E8%7D%5C%5C%5CRightarrow%20B%3D1.56421%5Ctimes%2010%5E%7B-6%7D%5C%20T)
The amplitude of the magnetic field at this surface is ![1.56421\times 10^{-6}\ T](https://tex.z-dn.net/?f=1.56421%5Ctimes%2010%5E%7B-6%7D%5C%20T)
Because some scientific theories are true and some are false