Question

# What is the total energy transported per hour along a narrow cylindrical laser beam 2.00 mm...

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 ?

given data

Brms= 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 εo Erms2

here     Erms= cBrms

so

intensity I = c εo (cBrms)2 =c3 εoBrms2

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 εoBrms2 πr2t                 (FORMULA)

εo=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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