A beam of polarized light with an average intensity of 13.5 W/m² is sent through a polarizer. The transmission axis makes an angle of 22.0° with respect to the direction of polarization. Determine the rms value of the magnetic field of the transmitted beam.

Brms = (2.205 × 10⁻⁷) T

Explanation:

The relationship between rms magnetic field and the intensity of the electromagnetic wave is given as

I = (Erms × Brms)/μ₀

where Erms = rms Electric field of the electromagnetic beam

Brms = rms magnetic field of the electromagnetic beam

μ₀ = magnetic constant = (4π × 10⁻⁷) H/m

But Erms is related to Brms through the relation

Erms = c × Brms

where c = speed of light = (3 × 10⁸) m/s

And the intensity of polarized light (I) is related to the initial intensity of polarized light (I₀), through the relationship

I = I₀ cos² θ

where θ = angle the transmission axis makes with respect to the direction of polarization = 22.0°

I₀ = initial intensity of unpolarized light = 13.5 W/m²

I = (Erms × Brms)/μ₀ becomes

I₀ cos² θ = (c × Brms²)/μ₀

Brms² = (μ₀ × I₀ cos² θ)/c

Brms² = (4π × 10⁻⁷ × 13.5 × cos² 22°)/(3 × 10⁸)

Brms² = 4.861 × 10⁻¹⁴

Brms = 0.0000002205 = (2.205 × 10⁻⁷) T

Hope this Helps!!!

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