Problem with electromagnetic waves

[andrew410]

Lasers have been used to suspend spherical glass beads in the Earth's gravitational field. a) A black bead has a mass of 1 micrograms and a density of 0.200 g/cm^3. Determine the radiation intensity needed to support the bead. b) If the beam has a radius of 0.200 cm, what is the power required for this laser.

I know that density = mass/volume, so I can get the volume from the density and mass. I know that the energy density = energy/volume. Also, I know that intensity = speed of light*energy density. How do I get the energy or am I doing this wrong? Please help...any help would be great! thx! :)

 

[Astronuc]

Well, the magnitude force needed to suspend the micro-ball must = mg.

The magnitude of the force is related to Pressure x area, but remember this is a curved surface, and one needs the force operating anti-parallel to gravity.

In another of your posts, there is a discussion of radiation (light) pressure. The pressure is simply due to momentum transfer. Consider the relationship between energy and momentum for light.

 

[thepatientmental]

a) To determine the radiation intensity needed to support the bead, we can use the equation for gravitational force:

F = mg = (1 microgram)(9.8 m/s^2) = 9.8 x 10^-6 N

This force must be balanced by the radiation pressure from the laser beam. The equation for radiation pressure is:

P = I/c, where P is pressure, I is intensity, and c is the speed of light.

Since we want to find the intensity, we can rearrange the equation to solve for I:

I = Pc

Now, we need to find the power of the laser in order to calculate the intensity. This will be done in part b.

b) To find the power required for the laser, we can use the equation:

P = Fv, where P is power, F is force, and v is velocity.

In this case, the velocity is the speed of light, so we can rewrite the equation as:

P = Fc

Substituting in the value for force from part a, we get:

P = (9.8 x 10^-6 N)(3.00 x 10^8 m/s) = 2.94 x 10^-3 W

Therefore, the power required for the laser to support the black bead is 2.94 x 10^-3 W.

Now, to find the intensity, we can plug this value into the equation from part a:

I = Pc = (2.94 x 10^-3 W)(3.00 x 10^8 m/s) = 882 W/m^2

This is the radiation intensity needed to support the black bead.