A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the e

Question

A lamp emits monochromatic green light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes 100 W of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly:

TestHub · Accepted Answer

Wavelength of monochromatic green light ​ = 5.5 × 1 0 − 5 cm Intensity I = Area Power ​ = 4 π ( 5 ) 2 100 × ( 3/100 ) ​ = 100 π 3 ​ Wm − 2 ​ Now, half of this intensity (I) belongs to electric field and half of that to magnetic field, therefore, ​ 2 I ​ = 4 1 ​ ε 0 ​ E 0 2 ​ C or E 0 ​ = ε 0 ​ C 2 I ​ ​ ​ ​ = ( 4 π × 9 × 1 0 9 1 ​ ) × ( 3 × 1 0 8 2 × ( 100 3 ​ π ) ​ ​ = 25 6 ​ × 30 ​ = 7.2 ​ ∴ E 0 ​ = 2.68 V / m ​

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