A 5.00-mW laser pointer has a beam diameter of 2.00 mm a) What is the root-mean-square value of

step 1 Then we have power of a laser p equals to 5 .00 mmlipatt that is 5 .00 multiplicate by 10 to the

A 5.00-mW laser pointer has a beam diameter of 2.00 mm a)...

A $5.00-\mathrm{mW}$ laser pointer has a beam diameter of $2.00 \mathrm{~mm}$
a) What is the root-mean-square value of the electric field in this laser beam?
b) Calculate the total electromagnetic energy in $1.00 \mathrm{~m}$ of this laser beam.

Key Concepts

Beam Cross-sectional Area and Energy Content

For a laser beam, the total electromagnetic energy contained in a segment of the beam is determined by multiplying the energy density by the beam's cross-sectional area and the length of the segment. The cross-sectional area is typically computed from the beam diameter assuming a circular profile, using the formula A = ? (d/2)².

Relation Between Electric Field and Energy Density

The energy carried by an electromagnetic wave is stored in its electric and magnetic fields. For a plane wave, the time-averaged energy density can be expressed in terms of the rms electric field as u = ?? E_rms². This relationship allows one to determine the electromagnetic energy per unit volume from the electric field strength.

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space at the speed of light. Their energy transport and oscillatory properties are described by Maxwell's equations, and they are characterized by properties such as frequency, wavelength, and intensity.

Intensity and the Poynting Vector

Intensity is a measure of the power transmitted per unit area by an electromagnetic wave. It is quantified using the Poynting vector, whose time?averaged magnitude is related to the root-mean-square (rms) value of the electric field by the relation I = (1/2) c ?? E_rms² for a sinusoidal wave, where c is the speed of light and ?? is the permittivity of free space.

Transcript

Please give Ace some feedback