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}
Erms^{2}**

**here **
**E _{rms}= cB_{rms}**

**so**

**intensity I = c ε _{o}
(cB_{rms})^{2} =c^{3}
ε_{o}B_{rms}^{2}**

**and we know that**

**intesnity I = P/A**

**P= POWER**

**A= AREA**

**AND P= Energy/time = E/t**

**P=E/t**

**since area A=**
**π****r ^{2}**

**finally**

**intensity I = P/A =E/At =**

**I = E / At**

**energy E = IAt = c ^{3}
ε_{o}B_{rms}^{2}**

**ε _{o}=8.85x10^{-12}
C^{2}/Nm^{2}**

**Area = A = π****r ^{2} =
(3.142)(1.0X10^{-3})^{2} = 3.142X10^{-6}
m^{2}**

**c=3X10 ^{8} m/s**

**t=3600 sec**

**plugging the values in formula**

**energy E per hour = (3X10 ^{8}
m/s)^{3}**(

**energy per hour is = 3.2719x10 ^{-8}
J**

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