2 Marks Questions - Physics STD 12 Science Questions - Vidyadip

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Question 12 Marks

The magnetic field in a plane electromagnetic wave is given by $B_y=\left(2 \times 10^{-7}\right) T \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right)$.
(a) What is the wavelength and frequency of the wave?
(b) Write an expression for the electric field.

Answer

(a) Comparing the given equation with
$
B_y=B_0 \sin \left[2 \pi\left(\frac{x}{\lambda}+\frac{t}{T}\right)\right]
$
We get, $\lambda=\frac{2 \pi}{0.5 \times 10^3} m =1.26 cm$, and
$
\frac{1}{T}=\nu=\left(1.5 \times 10^{11}\right) / 2 \pi=23.9 GHz
$

(b) $E_0=B_0 c=2 \times 10^{-7} T \times 3 \times 10^8 m / s =6 \times 10^1 V / m$
The electric field component is perpendicular to the direction of propagation and the direction of magnetic field. Therefore, the electric field component along the $z$-axis is obtained as $E_z=60 \sin \left(0.5 \times 10^3 x+1.5 \times 10^{11} t\right) V / m$

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Question 22 Marks

Identify the electromagnetic waves whose wavelengths lie in the range:

10^–11 m < $\lambda$ < 10^–14 m
10^–4 m < $\lambda$ < 10^–6 m

Write one use for each.

Answer

X – rays/Gamma rays.

One use of the name given.

Infrared/Visible/Microwave.

One use of the name given.

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Question 32 Marks

Identify the electromagnetic waves whose wavelengths vary as

10^{–12 m} < $\lambda$ < 10^–8 m
10^{–3 m} < $\lambda$ < 10^–1 m

Write one use for each.

Answer

X – rays

Used for medical purposes.

Microwaves

Used in radar systems.

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Question 42 Marks

Draw a sketch of a plane electromagnetic wave propagating along the z-direction. Depict clearly the directions of electric and magnetic fields varying sinusoidally with z.

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Question 52 Marks

How does Ampere-Maxwell law explain the flow of current through a capacitor when it is being charged by a battery? Write the expression for the displacement current in terms of the rate of change of electric flux.

Answer

During charging, electric flux between the plates of capacitor keeps on changing; this results in the production of a displacement current between the plates.
$Id=\in_0\frac{d\phi_E}{dt}\big(Id=\in_0A\frac{dE}{dt}\big)$

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Question 62 Marks

An em wave is travelling in a medium with a velocity $\overrightarrow{\text{v}} = \text{v}\hat{\text{i}}.$ Draw a sketch showing the propagation of the em wave, indicating the direction of the oscillating electric and magnetic fields.
How are the magnitudes of the electric and magnetic fields related to the velocity of the em wave?

Answer

$\frac{\text{E}_{0}}{\text{B}_{0}} = \text{c}.$

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Question 72 Marks

How are infrared waves produced? Why are these referred to as 'heat waves'? Write their one important use.

Answer

Method of production
by hot bodies and molecules/due to vibrations of atoms and molecules/due to transition of electrons between two (closely spaced) energy levels in an atom.
Infrared waves are called heat waves as they cause heating effect/rise in temperature
Maintains earth's warmth, physical therapy, remote switches etc.

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Question 82 Marks

Arrange the following electromagnetic radiations in ascending order of their frequencies:

Microwave.
Radio wave.
X-rays.
Gamma rays.

Write two uses of any one of these.

Answer

Radio waves < Microwaves < X-rays < Gamma rays.

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Question 92 Marks

How does a charge q oscillating at certain frequency produce electromagnetic waves?

Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave propagating along the Z-direction.

Answer

Oscillating charge produces an oscillating electric field in space, which produces an oscillating magnetic field, which in turn, is a source of oscillating electric field, and so on.

Alternate Answer

An oscillating electric charge produces self sustaining oscillations of electric and magnetic field in free space or vacuum.

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Question 102 Marks

The oscillating magnetic field in a plane electromagnetic wave is given by

$\text{B}_{y} = ( 8 \times 10^{-6}) sin [2\times 10 ^{11}t + 300 \pi\text{x}] T$.

Calculate the wavelength of the electromagnetic wave.
Write down the expression for the oscillating electric field.

Answer

(HOTS)

Comparing the given expression with.

$\text{B}_{y} = \text{B}_{\circ}sin\bigg(\frac{4\pi\text{t}}{T} - \frac{2\pi}{\lambda}\bigg)$

Alternate Answer

$\text{B}= \text{B}_{\circ} \sin \big(\omega\text{t} + kx\big)$

we get

$\therefore \text{k} \frac{2 \pi}{\lambda} = 300 \pi$

$\therefore \lambda = \frac{1}{150}m$ or $ \frac{2}{3} cm $ or 0.67 cm

$\text{E}_{Z} = \text{E}_{\circ} sin ( 2 \times 10^{11}t + 300 \pi\text{x})\text{Vm}^{-1}$

$ = 2400 sin ( 2 \times 10^{11}t + 300 \pi\text{x})\text{Vm}^{-1}$

Alternate Answer

$\text{E}_{z} = \text{c}\times8 \times 10 ^{-6} sin ( 2 \times10^{11}t + 300 \pi\text{x})\text{Vm}^{-1}$

Award full mark if either of the second or third line expression is written without writing the first line.

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Question 112 Marks

Why are infra-red waves often called heat waves? Explain.
What do you understand by the statement, ‘‘Electromagnetic waves transport momentum’’?

Answer

Infrared waves are prdocued by vibration of atoms of molecules which increases the temperature due which they are also the cause of heat energy.
Electromagnetic waves also show particle nature, i.e., they aslo behave as a matter according to Planks Quantum theory, So, they also possess some momentum and they can also change momentum.

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Question 122 Marks

Long distance radio broadcasts use short wave bands, why?

Answer

Radio broadcasts use the reflection of transmitted waves through different ionospheric layers. These layers reflect short wavelength bands.

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Question 132 Marks

About 5% of the power of a 100 W light bulb is converted to visible radiation. What is the average intensity of visible radiation

at a distance of 1m from the bulb?
at a distance of 10 m?

Assume that the radiation is emitted isotropically and neglect reflection.

Answer

Power rating of bulb, P = 100 W

It is given that about 5% of Its power Is converted Into visible radiation.

$\therefore$ Power of visible radiation,

$\text{P}'=\frac{5}{100}\times100=5 \ \text{W}$

Hence, the power of visible radiation is 5W.

Distance of a point from the bulb, d = 1 m

Hence, intensity of radiation at that point is given as:

$\text{I}=\frac{\text{P}'}{4\pi\text{d}^2}$

$=\frac{5}{4\pi(1)^2}=0.398 \ \text{W}/\text{m}^2$

Distance of a point from the bulb, d₁ = 10 m

Hence, intensity of radiation at that point is given as:

$\text{I}=\frac{\text{P}'}{4\pi(\text{d}_1)^2}$

$=\frac{5}{4\pi(10)^2}=0.00398 \ \text{W}/\text{m}^2$

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Question 142 Marks

Why does microwave oven heats up a food item containing water molecules most efficiently?

Answer

The microwave oven heats up the food items containing water molecules most efficiently because the frequency of microwaves matches the resonant frequency of water molecules.

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Question 152 Marks

Which of the following can act as a source of electromagnetic waves:

A charge moving with a constant velocity.
A charge moving in a circular orbit.
A charge at rest.

Give reason.

Answer

Only an accelerated charge can radiate electromagnetic waves. As charge moving in a circular orbit is accelerated, so it can radiate electromagnetic waves.

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Question 162 Marks

Show that the dimensions of the displacement current $\in_0\frac{\text{d}\phi_\text{E}}{\text{dt}}$ are that of an electric current.

Answer

$\frac{\in_0\text{d}\phi_\text{E}}{\text{dt}}=\frac{\in_0\text{EA}}{\text{dt}4\pi\in_0\text{r}^2}$
$=\frac{\text{M}^{-1}\text{L}^{-3}\text{T}^4\text{A}^2}{\text{M}^{-1}\text{L}^{-3}\text{A}^2}\times\frac{\text{A}^1\text{T}^1}{\text{L}^2}\times\frac{\text{L}^2}{\text{T}}=\text{A}^1$
$=\text{(Current)}$ Proved.

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Question 172 Marks

Why is the orientation of the portable radio with respect to broadcasting station important?

Answer

The electromagnetic waves are plane polarised, so the receiving antenna should be parallel to the vibration of the electric or magnetic field of the wave. So the receiving antenna should be parallel to electric/magnetic part of the wave. That is why the orientation of the portable radio with respect to broadcasting station is important.

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Question 182 Marks

A charged particle oscillates about its mean (equilibrium) position with a frequency of 10⁹Hz. What is the frequency of the electromagnetic waves produced by the oscillator?

Answer

According to Maxwell’s theory, an oscillating charged particle with a frequency ν radiates electromagnetic waves of frequency ν.
So the frequency of electromagnetic waves produced by the oscillator is ν = 10⁹Hz.

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Question 192 Marks

A parallel plate capacitor made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad s_^-1.

What is the rms value of the conduction current?
Is the conduction current equal to the displacement current?
Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Answer

Radius of each circular plate, R = 6.0 cm = 0.06 m

Capacitance of a parallel plate capacitor, C = 100 pF = 100 × 10^-12 F

Supply voltage, V = 230 V

Angular frequency, ω = 300 rad s^-1

$=\frac{\text{V}}{\text{X}_\text{C}}$

Rms value of conduction current, I

Where,

XC = Capacitive reactance

$=\frac{1}{\omega\text{C}}$

$\therefore \ \text{I}=\text{V}\times\omega\text{C}$

$=230\times300\times100\times10^{-12}$

$=6.9\times10^{-6}\text{A}$

$=6.9\mu\text{A}$

Hence, the rms value of conduction current is 6.9 µA.

Yes, conduction current is equal to displacement current.
Magnetic field is given as:

$\text{B}=\frac{\mu_0\text{r}}{2\pi\text{R}^2}\text{I}_0$ Where,

µ₀ = Free space permeability $=4\pi\times10^{-7}\text{N}\text{A}^{-2}$

I₀ = Maximum value of current$=\sqrt2 \ \text{I}$

r = Distance between the plates from the axis = 3.0 cm = 0.03 m $\therefore$ B

$=\frac{4\pi\times10^{-7}\times\sqrt2\times6.9\times10^{-6}}{2\pi\times(0.03)^2}$

$=1.63\times10^{-11}\text{T}$

Hence, the magnetic field at that point is $1.63\times10^{-11}\text{T}$.

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Question 202 Marks

Find the wavelength of electromagnetic waves of frequency 5 × 1019Hz in free space. Give its two applications.

Answer

$\text{Wavelength},\lambda=\frac{\text{c}}{\nu}=\frac{3\times10^8}{5\times10^{19}}=6\times10^{-12}\text{m}$
These are gamma rays.
These are used for:

Nuclear reactions,
Radiotherapy.

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Question 212 Marks

The charge on a parallel plate capacitor varies as $\text{q}=\text{q}_0\cos2\pi\text{vt}$. The plates are very large and close together (area = A, separation = d). Neglecting the edge effects, find the displacement current through the capacitor?

Answer

The displacement current through the capacitor is given by,
$\text{I}_\text{d}=\text{I}_\text{c}=\frac{\text{dq}}{\text{dt}}\ .....(\text{i})$
Here we are given, $\text{q}=\text{q}_0\cos2\pi\text{vt}$
Putting this value in Eq (i), we get
$\text{I}_\text{d}=\text{I}_\text{c}=-\text{q}_0\sin2\pi\text{vt}\times2\pi\text{v}$
$\text{I}_\text{d}=\text{I}_\text{c}=-2\pi\text{vq}_0\sin2\pi\text{vt}$

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Question 222 Marks

Find the wavelength of electromagnetic waves of frequency 4 × 109Hz in free space. Give its two applications.

Answer

$\text{Wavelength},\lambda=\frac{\text{c}}{\nu}=\frac{3\times10^8}{4\times10^9}=\frac{3}{40}\text{m},$
$=\frac{300}{40}\text{cm}=7.5\text{cm}.$
This wavelength corresponds to microwave region (or short radio waves).
These are used in:

RADAR,
Microwave ovens.

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Question 232 Marks

What physical quantity is the same for Χ-rays of wavelength 10^-10m, red light of wavelength $6800\mathring{\text{A}}$ and radio waves of wavelength 500m?

Answer

Χ-rays, red light and radio waves are all electromagnetic waves. The speed of propagation in vacuum is the same for all these waves. This speed is equal to c = 3 × 108m/ s.

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