The maximum electric field 10 m from an isotropic point source of light is 2.0 V / m. What are

step 1 In this question, we are given a point source, okay, and then at 10 meters away from it, the EM

The maximum electric field 10 m from an isotropic point...

The maximum electric field $10 \mathrm{~m}$ from an isotropic point source of light is $2.0 \mathrm{~V} / \mathrm{m}$. What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?

Key Concepts

Electric and Magnetic Field Relationship

In electromagnetic waves, the electric and magnetic fields are related by the speed of light. Specifically, in free space, the maximum values of the fields satisfy the relation E = cB, where c is the speed of light. This relationship is fundamental in understanding how electromagnetic energy is partitioned between the electric and magnetic field components.

Intensity of Electromagnetic Waves

Intensity in an electromagnetic wave refers to the average energy transmitted per unit area per unit time. It can be expressed in terms of the electric field as I = (1/2)??cE?² or in terms of the magnetic field as I = (1/2)(B?²/??), where ?? and ?? are the permittivity and permeability of free space, respectively. This concept is critical for quantifying the energy flow in light and other electromagnetic radiation.

Inverse Square Law for Isotropic Sources

For an isotropic source, which radiates uniformly in all directions, the intensity of the radiation decreases with the square of the distance from the source. This is expressed by the formula I = P/(4?r²), emphasizing that as the distance increases, the energy spreads out over a larger spherical surface area, leading to a decrease in intensity.

Power of an Isotropic Emitter

The total power emitted by an isotropic source is related to the intensity measured at a distance by integrating over the entire sphere surrounding the source. Consequently, if the intensity at a distance is known, the power can be calculated using the formula P = I(4?r²), which represents the total energy output per unit time.

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