Answer:
(a) 3107.98 J
(b) 14530.6 J
Explanation:
mass, m = 3.56 kg
angular speed, ω = 179 rad/s
Moment of inertia of solid cylinder, I = 1/2 mr^2
where, m is the mass and r be the radius of the cylinder.
(a) radius, r = 0.330 m
I = 0.5 x 3.56 x 0.330 x 0.330 = 0.194 kgm^2
The formula for the rotational kinetic energy is given by
K = 0.5 x 0.194 x 179 x 179 = 3107.98 J
(b) radius, r = 0.714 m
I = 0.5 x 3.56 x 0.714 x 0.714 = 0.907 kgm^2
The formula for the rotational kinetic energy is given by
K = 0.5 x 0.907 x 179 x 179 = 14530.6 J
Answer: 8.6 µm
Explanation:
At a long distance from the source, the components (the electric and magnetic fields) of the electromagnetic waves, behave like plane waves, so the equation for the y component of the electric field obeys an equation like this one:
Ey =Emax cos (kx-ωt)
So, we can write the following equality:
ω= 2.2 1014 rad/sec
The angular frequency and the linear frequency are related as follows:
f = ω/ 2π= 2.2 1014 / 2π (rad/sec) / rad = 0.35 1014 1/sec
In an electromagnetic wave propagating through vacuum, the speed of the wave is just the speed of light, c.
The wavelength, speed and frequency, are related by this equation:
λ = c/f
λ = 3.108 m/s / 0.35. 1014 1/s = 8.6 µm.
Hello!
Distance of R/2:
Since a conducting sphere is referenced in this situation, all of its charge will be distributed along its SURFACE. Therefore, there is NO enclosed at a distance of R/2 from the center.
Using Gauss's Law:
E = Electric field strength (N/C)
A = Area of Gaussian surface (m²)
Q = Enclosed charge (C)
ε₀ = Permittivity of free space C²/Nm²)
If the enclosed charge is 0, then:
Distance of '2R':
We can once again use Gauss's Law to solve. This time, however, a surface of radius '2R' encloses ALL of the charge of the sphere.
'A' is equivalent to the surface area of a sphere of radius '2R', or:
Substituting this expression back into Gauss's Law:
To simplify:
OR using k = 1/4πε₀:
The concept passing a current through the loop applies the principle of the Ampere's Law. Ampere's law is commonly applied to electricity and magnetism in which it states that "<span>for any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop."</span>