A lamp emits monochromatic green light uniformly in all...

A lamp emits monochromatic green light uniformly in all directions. The lamp is $3 \%$ efficient in converting electrical power to electromagnetic waves and consumes $100 \mathrm{~W}$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $10 \mathrm{~m}$ from the lamp will be (A) $1.34 \mathrm{~V} / \mathrm{m}$ (B) $2.68 \mathrm{~V} / \mathrm{m}$ (C) $5.36 \mathrm{~V} / \mathrm{m}$ (D) $9.37 \mathrm{~V} / \mathrm{m}$

A lamp emits monochromatic green light uniformly in all directions. The lamp is $3 \%$ efficient in converting electrical power to electromagnetic waves and consumes $100 \mathrm{~W}$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $10 \mathrm{~m}$ from the lamp will be
(A) $1.34 \mathrm{~V} / \mathrm{m}$
(B) $2.68 \mathrm{~V} / \mathrm{m}$
(C) $5.36 \mathrm{~V} / \mathrm{m}$
(D) $9.37 \mathrm{~V} / \mathrm{m}$

Key Concepts

Poynting Vector and Electric Field Amplitude Relation

The Poynting vector quantifies the directional energy flux of an electromagnetic field, linking the intensity of the radiation to its electric and magnetic field components. The amplitude of the electric field is related to the intensity by a factor that includes fundamental electromagnetic constants such as the vacuum permittivity and the speed of light.

Intensity of Electromagnetic Waves

Intensity in the context of electromagnetic waves is defined as the power per unit area. This concept is vital for understanding how the power output of a light source is distributed over space and is used to calculate the energy flux at a given distance from the source.

Inverse Square Law

The inverse square law describes how the intensity of a physical effect (such as light or sound) decreases with increasing distance from the source. Specifically, for a source emitting uniformly in all directions, the energy is spread over the surface area of a sphere, which grows as the square of the distance, thereby reducing the intensity proportionally.

Energy Conversion Efficiency

This concept refers to the fraction of input energy that is converted into the desired form of energy. In many physical systems, not all the supplied energy is used effectively; understanding efficiency is crucial when calculating the actual amount of energy available for further propagation or work.

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