Physics M.C.Q (1 Marks)

1. 0.043

Explanation:

Power = intensity × area

Intensity and area are given,

Power = 1.3 × 1.1KW

Energy = power × time

Time is 2.5hr

Energy = 1300 × 1.1 × 2.5 × 3600J

= 12870000J

$\text{Momentum}=\frac{\text{energy}}{\text{c}}$

$=\frac{12870000}{3\times10^8}$

$=0.043$

2. $\frac{\pi}{2}$

Explanation:

Axis of propagation always lie perpendicular to the plane of vibrations, therefor angle between them is $\frac{\pi}{2}$

4. Deflects and gradually comes to the original position in a time that is large compared to the time constant.

Explanation:

The compass needle deflects due to the presence of the magnetic field. Inside the capacitor, a magnetic field is produced when there is a changing electric field inside it. As the capacitor is connected across the battery, the charge on its plates at a certain time tis given by,

$\text{Q}=\text{CV}\Big(1-\text{e}^{-\tau/\text{RC}}\Big),$

Q = Charge developed on the plates of the capacitor.

R = Resistance of the resistor connected in series with the capacitor.

C = Capacitance of the capacitor.

V = Potential difference of the battery.

The time constant of the capacitor is given, $\tau=\text{RC}$

The capacitor keeps on charging up to the time $\tau$. The development of charge on the plates will be gradual after $​​\tau=\text{RC}$ The change in electric field will be up to the time the charge is developing on the plates of the capacitor. Thus, the compass needle deflects and gradually comes to the original position in a time that is large compared to the time constant.

4. E × B.

Solution:

Key concept: A changing electric field produces a changing magnetic field and vice versa which gives rise to a transverse wave known as electromagnetic wave. The time varying electric and magnetic field are mutually perpendicular to each other and also perpendicular to the direction of propagation of this wave. The electric vector is responsible for the optical effects of an EM wave and is called the light vector.

The direction of propagation of electromagnetic wave is perpendicular to both electric field vector $(\vec{\text{E}})$ and $\vec{\text{B}}$ magnetic field vector B, i.e., in the direction of $\vec{\text{E}}\times\vec{\text{B}}$.

Here, elecromagnetic wave is along the z-direction which is given by the cross product of E and B.

3. $0.025\mu\text{s}$

Explanation:

Time period, $\text{T}=\frac{1}{\text{v}}$

$\text{T}=\frac{1}{40\times10^6}$

$\Rightarrow\text{T}=0.25\mu\text{s}$

3. $\frac{\text{I}}{\text{c}}$

Explanation:

Momentum of a photon

$=\frac{\text{h}}{\lambda}=\frac{\text{h}}{\frac{\text{c}}{\text{v}}}=\frac{\text{hv}}{\text{c}}=\frac{\text{E}}{\text{c}}$

Momentum over unit area

$=\frac{\text{E}}{\text{Ac}}=\frac{\text{I}}{\text{c}}\Big[\text{I}=\frac{\text{E}}{\text{A}}\text{ For wave}\Big]$

Since surface is non reflecting, final momentum of photon = 0, change in momentum $=\frac{\text{I}}{\text{c}}$

So, force per unit area $=\frac{\text{I}}{\text{c}}$

Pressure of radiation $=\frac{\text{I}}{\text{c}}$

1. In the x direction and in phase with the $\overline{\text{E}}$ field

Explanation:

The wave equation for a plane electric wave traveling in the x direction in space is

$\frac{\delta^2\text{E}}{\delta^2\text{y}}=\frac{1}{\text{c}^2}\frac{\delta^2\text{E}}{\delta\text{t}^2}$

with the same form applying to the magnetic field wave in a plane perpendicular the electric field. Both the electric field and the magnetic field are perpendicular to the direction of travel y.

1. $1.8\times10^{-8}\frac{\text{C}}{\text{s}}$

Explanation:

The displacement current is that current which comes into play in the region in which the electric field and hence the electric flux is changing with time.
Maxwell found that conduction current (I) and displacement current (I_d​) together have the property of continuity, although individually they may not be continuous. Maxwell also predicted that this current produces the same magnetic field as a conduction current can produce.
Displacement current is given by 

$\text{I}_\text{d}=\frac{\text{dq}}{\text{dt}}=1.8\times10^{-8}\frac{\text{C}}{\text{s}}$

1. Both A and B are true.

Explanation:

For a linearly polarised, plane electromagnetic wave,

$\text{E}=\text{E}_0\sin\omega\Big(\text{t}-\frac{\text{x}}{\text{c}}\Big)$

$\text{B}=\text{B}_0\sin\omega\Big(\text{t}-\frac{\text{x}}{\text{c}}\Big)$

The average value of either E or Bover a cycle is zero (average of $\sin(\theta)$ over a cycle is zero).

Also the electric energy density (U_E) and magnetic energy density (U_B)are equal.

$\text{u}_\text{E}=\frac{1}{2}\in_0\text{E}^2=\frac{\text{B}^2}{2\mu_0}=\text{u}_\text{B}$

Energy can be found out by integrating energy density over the entire volume of full space. As the energy of the electromagnetic wave is equally shared between electric and magnetic field so their average values will also be equal.

1. 8_p × 107

Explanation:

Frequency of wave f = 40 × 106 Hz

Angular frequency, $\omega=2\pi\text{v}$

$\omega=2\pi\times40\times10^6$

$\Rightarrow\omega=8\pi\times10^7\frac{\text{rad}}{\text{s}}$