Question 178: EM waves

Question

A radiation is emitted by 1000W bulb and it generates an electric field and magnetic field at P, placed at a distance of 2m. The efficiency of the bulb is 1.25%. The value of peak electric field at P is x $$	imes$$ 10$$-$$1 V/m. Value of x is ___________. (Rounded off to the nearest integer) [Take $${\varepsilon _0} = 8.85 	imes {10^{ - 12}}$$ C2N$$-$$1 m$$-$$2, c = $$3 	imes {10^8}$$ ms$$-$$1]

Accepted Answer

Intensity of electro magnetic wave is,
$$I = {1 \over 2}c{\varepsilon _0}E_0^2 = {P \over {4\pi {r^2}}}$$
$${1 \over 2}4\pi {\varepsilon _0} 	imes c 	imes E_0^2 = {P \over {{r^2}}}$$
$${1 \over 2} 	imes {{3 	imes {{10}^5} 	imes E_0^2} \over {9 	imes {{10}^9}}} = {{1000 	imes 1.25} \over {{{(2)}^2}}} 	imes {1 \over {100}}$$
$$E_0^2 = {{60 	imes 1000 	imes 1.25} \over {4 	imes 100}} = {{125 	imes 3} \over 2}$$
$$E_0^2 = {{375} \over 2} = 187.5$$
$${E_0} = 13.69$$
$${E_0} \approx 137 	imes {10^{ - 1}}$$ v/m

EM waves

Choose the correct answer: