A uniform laser beam of power 50 mW is propagating in free space. If the diameter of the beam is 4 mm (at a particular position), the amplitude of the electric field is approximately - 2.99 x 106 V/m 1.732 x 103 V/m 2.99 x 103 V/m 1.732 x 106 V/m

The intensity (I) of the laser beam can be calculated using the formula:

I = P/A

where P is the power of the laser beam and A is the cross-sectional area of the beam.

Given that the power P is 50 mW or 50 x 10^-3 W, and the diameter of the beam is 4 mm or 4 x 10^-3 m, we can calculate the area A using the formula for the area of a circle (πr^2), where r is the radius of the beam (half the diameter):

A = πr^2 = π(2 x 10^-3 m)^2 = 4π x 10^-6 m^2

Substituting these values into the formula for intensity gives:

I = (50 x 10^-3 W) / (4π x 10^-6 m^2) = 3.98 x 10^3 W/m^2

The intensity of an electromagnetic wave is also given by the formula:

I = 0.5εcE^2

where ε is the permittivity of free space (8.85 x 10^-12 C^2/Nm^2), c is the speed of light (3 x 10^8 m/s), and E is the amplitude of the electric field.

Rearranging this formula to solve for E gives:

E = sqrt(2I / εc)

Substituting the known values gives:

E = sqrt[(2 x 3.98 x 10^3 W/m^2) / (8.85 x 10^-12 C^2/Nm^2 x 3 x 10^8 m/s)] = 1.732 x 10^6 V/m

So, the amplitude of the electric field is approximately 1.732 x 10^6 V/m.