Question

What is the total energy transported per hour along a narrow cylindrical laser beam 2.00 mm in diameter, whose B-field has an rms strength of 1.10 ×10−10 T ?

Answer 1

given data

B_rms= 1.10 ×10^-10 T

narrow cylindrical laser beam diameter = 2.0 mm = 2x10^-3 m

radius is r = d/2 = 1x10^-3 m

intensity I = c ε_o Erms²

here     E_rms= cB_rms

so

intensity I = c ε_o (cB_rms)² =c³ ε_oB_rms²

and we know that

intesnity I = P/A

P= POWER

A= AREA

AND P= Energy/time = E/t

P=E/t

since area A= πr²

finally

intensity I = P/A =E/At =

I = E / At

energy E = IAt = c³ ε_oB_rms² πr²t                 (FORMULA)

ε_o=8.85x10^-12 C²/Nm²

Area = A = πr² = (3.142)(1.0X10^-3)² = 3.142X10^-6 m²

c=3X10⁸ m/s

t=3600 sec

plugging the values in formula

energy E per hour = (3X10⁸ m/s)³(8.85x10^-12 C²/Nm²)(1.10 ×10^-10 T)²(3.142X10^-6)(3600)=3.2719x10^-8 J

energy per hour is = 3.2719x10^-8 J

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