First slide

Electromagnetic waves and its nature

Question

A lamp emits monochromatic light uniformly in all directions. The lamp is 3% efficient in converting electrical power to electromagnetic waves and consumes $100 W$ of electrical power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $10 m$ from the lamp will be

Moderate

A

$9.37 V m^{- 1}$
B

$5.36 V m^{- 1}$
C

$2.68 V m^{- 1}$
D

$1.34 V m^{- 1}$

Solution

Useful intensity, $I = \frac{p o w e r}{a r e a}$
$I = \frac{100 \times (3 / 100)}{4 π {(10)}^{2}} = \frac{3}{4 π \times 100} W m^{- 2}$
Half of this intensity (I) belongs to electric field and half of that to magnetic field .
Therefore,
$\frac{I}{2} = \frac{1}{4} \in_{0} E_{0}^{2} C \Rightarrow E_{0} = \sqrt{\frac{2 I}{\in_{0} C}}$
$\Rightarrow E_{0} = \sqrt{\frac{2 \times \frac{3}{4 π \times 100}}{\frac{1}{4 π \times 9 \times 10^{9}} \times 3 \times 10^{8}}} E_{0} = \sqrt{\frac{2 \times 3 \times 4 π \times 9 \times 10^{9}}{4 π \times 100 \times 3 \times 10^{8}}} = \sqrt{\frac{2 \times 9}{10}} = \frac{3}{\sqrt{5}} = 1.34 V m^{- 1}$

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