Question 174: EM waves

Question

The electric field in an electromagnetic wave is given by E = (50 NC
$$-$$1
) sin$$\omega$$ (t $$-$$ x/c)
The energy contained in a cylinder of volume V is 5.5 $$	imes$$ 10
$$-$$12
J. The value of V is _____________ cm
3
. (given $$\in$$
0
= 8.8 $$	imes$$ 10
$$-$$12
C
2
N
$$-$$1
m
$$-$$2
)

Accepted Answer

$$E = 50\sin \left( {\omega t - {\omega  \over c}.\,x} ight)$$
Energy density = $${1 \over 2}{ \in _0}E_0^2$$
Energy of volume $$V = {1 \over 2}{ \in _0}E_0^2.\,V = 5.5 	imes {10^{ - 12}}$$
$${1 \over 2}8.8 	imes {10^{ - 12}} 	imes 2500V = 5.5 	imes {10^{ - 12}}$$
$$V = {{5.5 	imes 2} \over {2500 	imes 8.8}} = .0005{m^3}$$
= .0005 $$	imes$$ 10
6
(c.m)
3
= 500 (c.m)
3

EM waves

The electric field in an electromagnetic wave is given by E = (50 NC $-1 ) sin\omega (t - x/c) The energy contained in a cylinder of volume V is 5.5 \times 10 -12 J. The value of V is _____________ cm 3 . (given \in 0 = 8.8 \times 10 -12 C 2 N -1 m -$2 )

Integer / Numeric Answer Type