Question

A $27\,mW$ laser beam has a cross-sectional area of ${10\,m{m^2}}$. The magnitude of the maximum electric field in this electromagnetic wave is given by? [Given permittivity of space ${\varepsilon _0} = 9 \times {10^{ - 12}}$ SI units, speed of light $c = 3 \times {10^8}\,m{s^{ - 1}}$ ]
A. $1\,kV{m^{ - 1}}$
B. $2\,kV{m^{ - 1}}$
C. $1.4\,kV{m^{ - 1}}$
D. $0.7\,kV{m^{ - 1}}$

Answer 1

Hint:Here we have to use the concept of intensity of EM wave to get the answer.Electromagnetic wave intensity is characterised as an energy transfer per second per unit area perpendicular to the propagation direction of electromagnetic waves.

Complete step by step answer:
Given, Power, $P = 27\,mW$
Area,$A = 10\,m{m^2}$
Permittivity of space ${\varepsilon _0} = 9 \times {10^{ - 12}}$ SI units
Speed of light $c = 3 \times {10^8}\,m{s^{ - 1}}$

We know that intensity of EM wave is given by:
$
I = \dfrac{{{\text{Power}}}}{{{\text{Area}}}}\\
\Rightarrow I= \dfrac{1}{2}{\varepsilon _ \circ }{E_ \circ }^2C \\
\Rightarrow \dfrac{{27 \times {{10}^{ - 3}}}}{{10 \times {{10}^{ - 6}}}} = \dfrac{1}{2} \times 9 \times {10^{ - 12}} \times {E^2} \times 3 \times {10^8} \\
\Rightarrow E = \sqrt 2 \times {10^3}\,kV{m^{ - 1}} \\
\therefore E = 1.4\,kV{m^{ - 1}} \\$
Hence, option C is correct.

Additional information:
In physics, radiant energy intensity is the power transmitted per unit area, where the area perpendicular to the direction of propagation of the energy is determined in the plane. It has units of watts per square metre in the SI system. Waves that are generated as a result of vibrations between an electrical field and a magnetic field are electromagnetic waves or EM waves. In other words, oscillating magnetic and electric fields are made of EM waves.

Note:Here we have to observe the units. If the units are not in standard form we need to convert them otherwise the answer would decrease by a factor of ten or hundred.Generally, a charged particle generates an electric field. On other charged particles, a force is applied by this electric field. In the direction of the field, positive charges accelerate and negative charges accelerate in the direction opposite to that of the field.