Question

A laser beam has intensity 2.5 xx (10^14)W (m^-2). Find the amplitudes of electric and magnetic fields in the beam.

Answer 1

C=E/B

And I=cμo(Erms)2

or, 2.5×1014=3×108×4π×10−7(Erms)2

∴Erms=30.7×107

Now, E=root2×Erms

=root2×30.7×107

=4.34×107NC−1

=4.34×108NC−1

∴B=E/C=3×1084.34×108

B=1.44T

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Answer 2

Given:

Intensity of laser $I = 2.5 \times 10^{14}$ $\frac{W}{m^{2} }$

To Find:

Amplitude of electric and magnetic field.

From the formula of intensity in terms of electric field,

    $I = \frac{1}{2} c\epsilon _{o} E^{2}$

Where $\epsilon _{o} = 8.85 \times 10^{-8}$

  $E = \sqrt{\frac{2I}{c \epsilon _{o} } }$

  $E = \sqrt{\frac{2 \times 2.5 \times 10^{14} }{3\times 10^{8} \times 8.85 \times 10^{-12} } }$

  $E = 4.33 \times 10^{8}$ $\frac{N}{C}$

From relation between electric field and magnetic field,

  $c = \frac{E}{B}$

The magnetic field is given by,

  $B = \frac{E}{c}$

  $B = \frac{4.33 \times 10^{8} }{3 \times 10^{8} }$                    ( $c = 3 \times 10^{8} \frac{m}{s}$ )

$B = 1.44$ T

Therefore, the amplitude of electric field and magnetic field is $4.33 \times 10^{8} \frac{N}{C}$ and 1.44 T respectively.