An electromagnetic wave of electric field E=10 sin(wt - kx) N/C is incident normal to the cross sectional area of cylinder 10 cm/m×m and having length 100 cm, lying along x-axis. Find energy density, energy contained in the cylinder, the intensity of the wave, momentum transferred to the cross sectional area of cylinder in 1 s considering total absorption and the radian pressure.

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Solution

Dear Student,
$w e k n o w e n e r g y d e n s i t y o f t h e E M w a v e = \frac{1}{2} ε_{0} {E_{0}}^{2} = \frac{1}{2} \times 8.85 \times 10^{- 12} \times 100 = 4.425 \times 10^{- 10} J m^{- 3} a s h e r e E_{0} = 10 V / m a n d e n e r g y c o n t a i n e d i n c y l i n d e r (U) = e n e r g y d e n s i t y \times v o l u m e o f t h e c y l i n d e r = 4.425 \times 10^{- 10} \times 10 \times 10^{- 4} \times 1 = 4.425 \times 10^{- 13} a n d i n t e n s i t y I = e n e r g y d e n s i t y \times s p e e d o f w a v e = 4.425 \times 10^{- 10} \times 3 \times 10^{8} = 0.13275 W / m^{2} m o m e n t u m t r a n s f e r e d p e r s e c o n d = e n e r g y d e n s i t y \times c r o s s s e c t i o n = 4.425 \times 10^{- 10} \times 10 \times 10^{- 4} = 4.425 \times 10^{- 13} N s a n d r a d i a t i o n p r e s s u r e = \frac{I}{c} = 4.425 \times 10^{- 10} p a$
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