The electric field in an electromagnetic wave is given by E=(50NC−1)sinω(t−xc). Find the electrical energy contained in a cylinder of cross-section 10 cm2 and length 50 cm along the x-axis.
A
5.5×10−12J
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B
1.1×10−8J
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C
5×10−4J
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D
1.1×10−12J
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Solution
The correct option is A5.5×10−12J Given that E=(50NC−1)sinω(t−xc) E0=50NC−1A=10cm2L=50cm Now we know energy density is given by UD=12ε0E20 ⇒UD=12×8.85×10−12×502 ⇒UD=1.1×10−8J/m3 So energy contained can be obtained by UT=UD×V where V is the volume ⇒UT=UD×A×L ⇒UT=1.1×10−8×50×10×10−4 ⇒UT=5.5×10−12J