Assuming all the energy from 1000 watt lampis radiated uniformly, calculate the average values of the intensities of electric field and magnetic field of radiation at a distance of 2m from the lamp?

Question

Answer

Calculation of Average Intensities of Electric and Magnetic Fields of Radiation

Given Data

Power of lamp, P = 1000 W

Distance from the lamp, r = 2 m

Calculation of Intensity

Intensity of radiation is given by the formula:

I = P / (4πr²)

Calculation of Electric Field Intensity

Electric field intensity is given by the formula:

E = (2I/μ₀)^(1/2)

Where μ₀ is the permeability of free space.

Therefore,

E = (2 * P / (4πμ₀r²))^(1/2)

Calculation of Magnetic Field Intensity

Magnetic field intensity is given by the formula:

B = (2I/ε₀c²)^(1/2)

Where ε₀ is the permittivity of free space and c is the speed of light.

Therefore,

B = (2 * P / (4πε₀r²c²))^(1/2)

Substituting Values

μ₀ = 4π × 10^-7 H/m

ε₀ = 8.854 × 10^-12 F/m

c = 3 × 10^8 m/s

Therefore,

E = (2 * 1000 / (4π × 4π × 10^-7 × 2²))^(1/2) = 11.20 V/m

B = (2 * 1000 / (4π × 8.854 × 10^-12 × (2 × 3 × 10^8)² × 2²))^(1/2) = 3.54 × 10^-10 T

Final Answer

Average Electric Field Intensity = 11.20 V/m

Average Magnetic Field Intensity = 3.54 × 10^-10 T

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