The electric field in an electromagnetic wave is given by E = (50… - Vidyadip

MCQ

The electric field in an electromagnetic wave is given by ${E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})$

The energy contained in a cylinder of volume ${V}$ is $5.5 \times 10^{-12} \, {J}$. The value of ${V}$ is $......{cm}^{3}$ $\left(\right.$ given $\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)$

A
$5000$
B
$1500$
✓
$500$
D
$100$

✓

Answer

Correct option: C.

$500$

c
${E}=50 \sin \left(\omega {t}-\frac{\omega}{{c}} \cdot {x}\right)$

Energy density $=\frac{1}{2} \in_{0} {E}_{0}^{2}$

Energy for volume ${V}=\frac{1}{2} \in_{0} {E}_{0}^{2} \cdot {V}=5.5 \times 10^{-12}$

$\frac{1}{2} 8.8 \times 10^{-12} \times 2500 {V}=5.5 \times 10^{-12}$

${V}=\frac{5.5 \times 2}{2500 \times 8.8}=.0005\, {m}^{3}$

$=.0005 \times 10^{6}\,({c} . {m})^{3}$

$=500({c} \, \cdot {m})^{3}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Which of the following is most unstable

$1$ mole of rigid diatomic gas performs a work of $Q / 5$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{ x R }{8},$ The value of $x$ is $\ldots \ldots \ldots .$ $[ K =$ universal gas constant $]$

If a satellite of mass $400 \,kg$ revolves around the earth in an orbit with speed $200 \,m / s$ then its potential energy is .......... $MJ$

If the length of potentiometer wire is increased, then the length of the previously obtained balance point will

A sample contains $10^{-2}\, kg$ each of two substances A and $B$ with half lives $4 \,s$ and $8 \,s$ respectively. The ratio of then atomic weights is $1: 2$ The ratio of the amounts of $A$ and $B$ after $16 \,s$ is $\frac{x}{100}$. the value of $x$ is........

In a system of particles, internal forces can change (for the system)

Two coils of self inductances $2\, mH$ and $8\, mH$ Hare placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is......$mH$

A wire of length $1 \,m$ is moving at a speed of $2\,ms^{-1}$ perpendicular to its length and a homogeneous magnetic field of $0.5\,T$. The ends of the wire are joined to a circuit of resistance $6$ $\Omega$ The rate at which work is being done to keep the wire moving at constant speed is

Radius of curvature of concave mirror is $40cm$ and the size of image is twice as that of object, then the object distance is....$cm$

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre. At some instant of time a viscous fluid of mass $m$ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period