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 electric power to electromagnetie waves and consume $100 \mathrm{~W}$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5 \mathrm{~m}$ from the lamp will be (a) $2.68 \mathrm{Vm}^{-1}$ (b) $3.15 \mathrm{Vm}^{-1}$ (c) $2.01 \mathrm{Vm}^{-1}$ (d) 0

A lamp emits monochromatic green light uniformly in all directions. The lamp is $3 \%$ efficient in converting electric power to electromagnetie waves and consume $100 \mathrm{~W}$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5 \mathrm{~m}$ from the lamp will be
(a) $2.68 \mathrm{Vm}^{-1}$
(b) $3.15 \mathrm{Vm}^{-1}$
(c) $2.01 \mathrm{Vm}^{-1}$
(d) 0

Key Concepts

Inverse Square Law

The inverse square law is a fundamental principle in physics that states that a specified physical quantity or intensity is inversely proportional to the square of the distance from the source. In the context of electromagnetic radiation, it explains how the power spreads out over a growing spherical surface area as the distance from the source increases, thus reducing the power per unit area.

Intensity and Electric Field Amplitude Relationship

In electromagnetic waves, there exists a well-defined relationship between the intensity (power per unit area) and the amplitude of the electric field. This relationship is derived from the energy density of the electromagnetic fields in free space and typically involves constants such as the vacuum permittivity and the speed of light. It allows one to compute the electric field strength if the intensity of the wave is known.

Spherical Wave Propagation

Spherical wave propagation describes how energy emitted uniformly from a point source spreads out in all directions. Due to this spreading, the intensity of the wave diminishes with the square of the distance from the source, following an inverse square law. This is important for calculating the intensity at any given distance from an isotropic emitter.

Energy Conversion Efficiency

This concept deals with the fraction of input energy (like electrical power) that is successfully converted into the desired form, such as electromagnetic radiation. Understanding efficiency is crucial in determining the actual amount of energy available for emission, as only a portion of the supplied power is converted and the rest is usually lost as heat or other forms of energy.

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