I think your question should be:
An industrial laser is used to burn a hole through a piece of metal. The average intensity of the light is
![S = 1.23*10^9 W/m^2](https://tex.z-dn.net/?f=%20S%20%3D%201.23%2A10%5E9%20W%2Fm%5E2%20)
What is the rms value of (a) the electric field and
(b) the magnetic field in the electromagnetic wave emitted by the laser
Answer:
a) ![6.81*10^5 N/c](https://tex.z-dn.net/?f=%206.81%2A10%5E5%20N%2Fc%20)
b) ![2.27*10^3 T](https://tex.z-dn.net/?f=%202.27%2A10%5E3%20T%20)
Explanation:
To find the RMS value of the electric field, let's use the formula:
![E_r_m_s = sqrt*(S / CE_o)](https://tex.z-dn.net/?f=%20E_r_m_s%20%3D%20sqrt%2A%28S%20%2F%20CE_o%29)
Where
;
;
![S = 1.23*10^9 W/m^2](https://tex.z-dn.net/?f=%20%20S%20%3D%201.23%2A10%5E9%20W%2Fm%5E2%20)
Therefore
![E_r_m_s = sqrt*{(1.239*10^9W/m^2) / [(3.00*10^8m/s)*(8.85*10^-^1^2C^2/N.m^2)]}](https://tex.z-dn.net/?f=%20E_r_m_s%20%3D%20sqrt%2A%7B%281.239%2A10%5E9W%2Fm%5E2%29%20%2F%20%5B%283.00%2A10%5E8m%2Fs%29%2A%288.85%2A10%5E-%5E1%5E2C%5E2%2FN.m%5E2%29%5D%7D%20)
![E_r_m_s= 6.81 *10^5N/c](https://tex.z-dn.net/?f=%20E_r_m_s%3D%206.81%20%2A10%5E5N%2Fc%20)
b) to find the magnetic field in the electromagnetic wave emitted by the laser we use:
;
;
![B_r_m_s = 2.27*10^3 T](https://tex.z-dn.net/?f=%20B_r_m_s%20%3D%202.27%2A10%5E3%20T%20)
Answer:
v = 10 m/s
Explanation:
Given,
Length of the vine, l = 36 m
Angle of inclination = 31.0◦ with the vertical
acceleration due to gravity = 9.81 m/s²
Using Conservation of energy
KE = PE
![\dfrac{1}{2} mv^2 = m g h](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B2%7D%20mv%5E2%20%3D%20m%20g%20h)
![v = \sqrt{2gh}](https://tex.z-dn.net/?f=%20v%20%3D%20%5Csqrt%7B2gh%7D)
![v = \sqrt{2 g l(1-\cos \theta)](https://tex.z-dn.net/?f=%20v%20%3D%20%5Csqrt%7B2%20g%20l%281-%5Ccos%20%5Ctheta%29)
![v = \sqrt{2\times 9.81\times 36 \times (1-\cos 31^0)](https://tex.z-dn.net/?f=%20v%20%3D%20%5Csqrt%7B2%5Ctimes%209.81%5Ctimes%2036%20%5Ctimes%20%281-%5Ccos%2031%5E0%29)
v = 10 m/s
Hence, the speed of the swing is equal to 10 m/s
Answer:
Momentum, p = 5 kg-m/s
Explanation:
The magnitude of the momentum of an object is the product of its mass m and speed v i.e.
p = m v
Mass, m = 3 kg
Velocity, v = 1.5 m/s
So, momentum of this object is given by :
![p=3\ kg\times 1.5\ m/s](https://tex.z-dn.net/?f=p%3D3%5C%20kg%5Ctimes%201.5%5C%20m%2Fs)
p = 4.5 kg-m/s
or
p = 5 kg-m/s
So, the magnitude of momentum is 5 kg-m/s. Hence, this is the required solution.
To develop this problem it is necessary to apply the concepts related to destructive interaction.
By definition we know that it is given as
![\Delta l = (m+\frac{1}{2})\lambda](https://tex.z-dn.net/?f=%5CDelta%20l%20%3D%20%28m%2B%5Cfrac%7B1%7D%7B2%7D%29%5Clambda)
Where,
l = Distance between slits
m = Any integer representing the number of repetition of spectrum
![\lambda = Wavelength](https://tex.z-dn.net/?f=%5Clambda%20%3D%20Wavelength)
There is a change in phase at the upper side of the film which causes the phase shift since the index of refraction of the soap film is greater than that of air.
The extra traveled distance is twice the film thickness since the light shines perpendicularly and the wave travels back and fourth through the film, so
![2t +\frac{1}{2} \lambda = (m+\frac{1}{2})\lambda](https://tex.z-dn.net/?f=2t%20%2B%5Cfrac%7B1%7D%7B2%7D%20%5Clambda%20%3D%20%28m%2B%5Cfrac%7B1%7D%7B2%7D%29%5Clambda)
![2t = m\lambda](https://tex.z-dn.net/?f=2t%20%3D%20m%5Clambda)
(second smalles nonzero thickness) we have that
![2t = 2\lambda](https://tex.z-dn.net/?f=2t%20%3D%202%5Clambda)
![t = \lambda](https://tex.z-dn.net/?f=t%20%3D%20%5Clambda)
The index of refraction of soap is given so the relationship is
![\lambda = \frac{\lambda{vacuum}}{n}](https://tex.z-dn.net/?f=%5Clambda%20%3D%20%5Cfrac%7B%5Clambda%7Bvacuum%7D%7D%7Bn%7D)
Substituting the previos equation
![t = \frac{\lambda_{vacuum}}{n}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clambda_%7Bvacuum%7D%7D%7Bn%7D)
Re, arrange to find \lambda_{vacuum}
![\lambda_{vacuum} = tn](https://tex.z-dn.net/?f=%5Clambda_%7Bvacuum%7D%20%3D%20tn)
![\lambda_{vacuum} = 443*1.33](https://tex.z-dn.net/?f=%5Clambda_%7Bvacuum%7D%20%3D%20443%2A1.33)
![\lambda_{vacuum} = 575.89nm](https://tex.z-dn.net/?f=%5Clambda_%7Bvacuum%7D%20%3D%20575.89nm)
Therefore the vacuum wavelength of the light is 575.89nm
Answer:
Mass = 4152kg
Explanation:
Given
L = 208m
I = 154A
V = 0.245V
Density = 3610 kg/m3
ρ = 4.23 x 10-8Ω·m = resistivity of wire
Resistance R = ρL/ A
R = voltage / current = V/I = 0.245/154 = 1.59×10-³ohms
1.59×10-³ = 4.23 x 10-⁸×208/A
Rearranging,
A = 4.23 x 10-⁸×208/1.59×10-³
A = 5.53×10-³m²
Mass = density × volume
Volume = L×A = 208×5.53×10-³m³= 1.15m³
Mass = 3610×1.15 = 4152kg