Question

High-power laser in factories are used to cut through cloth and metal. One such laser has a beam diameter of 1.00mm and generates an electric field having an amplitude 0.800MV/m at the target. Find(a) the amplitude of the magnetic field produced,(b) the intensity of the laser and (c) the power delivered by the laser.

Answer 1

(a) The amplitude of the magnetic field produced is 2.667 mV/m.

(b) The intensity of the laser is 2.832 W/m².

(c) The  power delivered by the laser is 2.22 x 10⁻⁶ W.

Amplitude of the magnetic field produced

In electromagnetic waves, the amplitude of magnetic field is the maximum field strength of the magnetic fields.

B₀ = E₀/c

where;

• E₀ is the amplitude electric field
• B₀ is the amplitude magnetic field
• c is speed of light

B₀ = (0.8 MV/m) / (3 x 10⁸)

B₀ = (0.8  x 10⁶ V/m) / (3 x 10⁸)

B₀ = 2.667 x 10⁻³ V/m

B₀ = 2.667 mV/m

Intensity of laser

The intensity of the laser is calculated as follows;

I = ¹/₂ε₀E₀²

I = (0.5)(8.85 x 10⁻¹²)(0.8 x 10⁶)²

I = 2.832 W/m²

power delivered by the laser

P = IA

where;

• A is the area of the beam

A = πd²/4

where;

• d is diameter

A = π(1 x 10⁻³)²/4

A = 7.854 x 10⁻⁷ m²

Power = (2.832 W/m²) x (7.854 x 10⁻⁷ m²)

Power = 2.22 x 10⁻⁶ W

Thus, the amplitude of the magnetic field produced is 2.667 mV/m.

The intensity of the laser is 2.832 W/m².

The  power delivered by the laser is 2.22 x 10⁻⁶ W.

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