During the testing of a new light bulb, a sensor is placed 17.7 cm from the bulb. It records a

step 1 During the testing of a new light bulb, a sensor is placed at a distance R equals to 17 .7 centi

During the testing of a new light bulb, a sensor is placed...

During the testing of a new light bulb, a sensor is placed $17.7 \mathrm{~cm}$ from the bulb. It records a root-mean-square value of $279.9 \mathrm{~V} / \mathrm{m}$ for the electric field of the radiation emitted from the bulb. What is the intensity of that radiation at the sensor's location?

Key Concepts

Electromagnetic Wave Intensity

This concept describes the power transmitted by an electromagnetic wave per unit area, typically measured in watts per square meter (W/m²). The intensity is directly related to the energy carried by the wave and is determined using the electric and magnetic field values. In free space, for a plane electromagnetic wave, the intensity is computed by combining constants such as the speed of light and the permittivity of free space with the square of the electric field's effective (rms) value.

Root-Mean-Square (RMS) Value

The RMS value is a statistical measure used to express the effective value of a varying quantity, such as the sinusoidally oscillating electric field in electromagnetic waves. Since the actual instantaneous values of the field oscillate over time, the RMS value provides a constant equivalent value in terms of power delivery, making it essential for practical measurements and calculations in AC circuits and wave phenomena.

Relationship Between Electric Field and Intensity

This key principle sets the connection between the measurable electric field strength and the intensity of the electromagnetic wave. In free space for a plane wave, the intensity is given by the formula I = c??(E_rms)², where c is the speed of light and ?? is the permittivity of free space. This relationship is fundamental in linking experimental observations (like the electric field reading) to the underlying energy flow in the radiation.

Inverse-Square Law

The inverse-square law explains how the intensity of radiation from a point source diminishes with the square of the distance from that source. Even though the calculation might use a measured field at a given distance, this law is crucial for understanding the overall distribution of light or radiation in space, as it predicts that the energy is spread out and becomes weaker as the distance from the source increases.

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