An observer is at 2 m from an isotropic point source of...

An observer is at $2 \mathrm{~m}$ from an isotropic point source of light emitting $40 \mathrm{w}$ power. The rm.s value of electric due to the source at the position of the observer is (A) $5.77 \times 10^{-8} \mathrm{Vm}^{-1}$ (B) $17.3 \mathrm{Vm}^{-1}$ (C) $57.7 \times 10^{-8} \mathrm{Vm}^{-1}$ (D) $1.73 \mathrm{Vm}^{-1}$

An observer is at $2 \mathrm{~m}$ from an isotropic point source of light emitting $40 \mathrm{w}$ power. The rm.s value of electric due to the source at the position of the observer is
(A) $5.77 \times 10^{-8} \mathrm{Vm}^{-1}$
(B) $17.3 \mathrm{Vm}^{-1}$
(C) $57.7 \times 10^{-8} \mathrm{Vm}^{-1}$
(D) $1.73 \mathrm{Vm}^{-1}$

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Key Concepts

Relationship Between Electric Field and Intensity

In electromagnetic theory, the intensity of a wave is related to the root mean square (rms) value of the electric field via the equation I = (1/2)c??E_rms². This formula connects the measurable field strength to the power distribution of the wave and is used to determine the rms electric field from the known intensity, thereby linking the macroscopic power output of the source with the microscopic oscillating fields.

Isotropic Point Source

An isotropic point source radiates energy uniformly in all directions, meaning that the power emitted is distributed equally over the surface area of a sphere centered at the source. This concept is critical in understanding how the intensity decreases with distance from the source as the same power is spread over a larger area.

Intensity of Electromagnetic Radiation

The intensity of radiation is defined as the power per unit area and, for an isotropic radiator, is calculated using the formula I = P/(4?r²), where P is the total power emitted by the source and r is the distance from the source. This principle helps in determining the energy available per unit area at a particular distance, which is essential for further calculations involving the electric field.

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