The electric field (in N C-1) in an electromagnetic wave is given by E=50 sin ω(t-(x/c)). The energy stored in a cylinder of cross-section 10 cm2 and length 100 cm along the x-axis will be

Question

The electric field (in N C-1) in an electromagnetic wave is given by E=50 sin ω(t-(x/c)). The energy stored in a cylinder of cross-section 10 cm2 and length 100 cm along the x-axis will be (A) 5.5 × 60-12 J (B) 1.1 × 10-11 J (C) 2.2 × 10-11 J (D) 1.65 × 10-11 J

Tardigrade Admin · Accepted Answer

Energy contained in a cylinder U = average energy density Ã volume =(1/2)ε0E20× Al =(1/2)×(8.85×10-12)×(50)2×(10×10-4)×1 =1.1×10-11 J

Q. The electric field (in $N C^{- 1}$ ) in an electromagnetic wave is given by $E = 50 s in ω (t - \frac{x}{c}) .$ The energy stored in a cylinder of cross-section $10 c m^{2}$ and length $100 c m$ along the x-axis will be

$5.5 \times 6 0^{- 12} J$

$1.1 \times 1 0^{- 11} J$

$2.2 \times 1 0^{- 11} J$

$1.65 \times 1 0^{- 11} J$

Energy contained in a cylinder
U = average energy density × volume
$= \frac{1}{2} ε_{0} E_{0}^{2} \times A l$
$= \frac{1}{2} \times (8.85 \times 1 0^{- 12}) \times (50)^{2} \times (10 \times 1 0^{- 4}) \times 1$
$= 1.1 \times 1 0^{- 11} J$

Q. The electric field (in NC−1) in an electromagnetic wave is given by E=50sinω(t−cx​). The energy stored in a cylinder of cross-section 10cm2 and length 100cm along the x-axis will be

5.5×60−12J

1.1×10−11J

2.2×10−11J

1.65×10−11J