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Multiple choice physics properties of material substances elastic behaviour of solids elastic and plastic substances properties of substances

The materials, which do not show a fixed trend of deformation vs. applied force, are called:

  1. inelastic materials

  2. plastic materials

  3. elastic materials

  4. rigid materials
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Elastic materials are those that follow the Hooke's law, which is that the deformation produced in a material is directly proportional to the stress applied to it, and the material is recoverable after the deformation force is removed.

Inelastic materials are those that do not follow this relationship. They do not show a fixed trend of deformation vs applied force; in fact, they might not deform at all (rigid materials) or the deformation observed is not completely recoverable.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

Choose the correct answer from the alternatives given.
A plane electromagnetic wave of frequency $25 MHz$ travels in free space along $X$-direction. At a particular point in space and time, electric field $\vec E=6.3\ \hat j\ V/m$. What is $B$ at this point.

  1. $1.2 \, \times \, 10^{-6} \, T$

  2. $1.2 \, \times \, 10^{-8} \, T$

  3. $2.1 \, \times \, 10^{-6} \, T$

  4. $2.1 \, \times \, 10^{-8} \, T$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given: The frequency of the electromagnetic wave is $25\ MHz$.

The electric field at the particular point is $6.3\hat j\ V/m$

To find: The magnetic field at that point.

The magnetic field of the electromagnetic wave at a point is given by:
$B = \dfrac{E}{c}\= \dfrac{6.3}{3 \times 10^8}\ \Rightarrow2.1 \times 10^{-8} T$

So, option $(D)$ is correct.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

The electric field of an electromagnetic wave traveling through the vacuum is given by the equation $E=E _0\ sin (Kx-\omega t).$ The quantity that is independent of wavelength is:

  1. $k\omega$

  2. $\dfrac{k}{\omega}$

  3. $k^2\omega$

  4. $\omega$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

To find: The quantity that is independent of the wavelength.


The angular frequency $\omega$ is given by:
$\omega \, = \, 2\pi \nu$
The frequency of a wave varies with the wavelength. So, angular frequency is dependent on wavelength.

The quantity $k$ is defined as the wavenumber and it is given by:
$k = \dfrac{2\pi}{\lambda}$
It shows that $k$ is dependent on wavelength.


The value of $\dfrac{k}{\omega}$ can be obtained as:
$\dfrac {k}{\omega} \, = \, \dfrac{2\pi / \lambda}{2\pi \nu}\\implies \, \dfrac{1}{\nu \lambda} \, = \, \dfrac{1}{c}\,\,\ \ \ \ \ \ \ \ \ \ \ \ \  (\because \, c \, = \, \nu \lambda)$
where c is the speed of electromagnetic wave in vacuum. It is a constant whose value is $3 \, \times \, 10^8 \, ms^{-1}$.

So, option $(B)$ is correct.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

Maxwell in his famous equations of electromagnetism, introduced the concept of

  1. ac current

  2. displacement current

  3. impedance

  4. reactance
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Maxwell's equations are:

1. $\nabla .E=\rho / \epsilon$
2. $\nabla.B=0$
3. $\nabla \times E= -\dfrac{dB}{dt}$
4. $\nabla \times B= \mu _0J+ \dfrac{1}{c^2} \dfrac{dE}{dt}$
so, considering the last eqn. written,
$\nabla \times B=\mu _0 J$ is the Ampere's eqn.
so, Maxwell modified the Ampere's eqn. and introduced the concept of displacement current.
So, displacement current =$\dfrac{1}{c^2} \dfrac{dE}{dt}$

Hence the correct option is $(B)$

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

A parallel plate capacitor of plate separation 2 mm is connected in an electric circuit having source voltage 400. What is the value of the displacement current for $10^{-6}$ s, if plate area is 60 $cm^2$

  1. $1.062 \times 10^{-2} \ A$

  2. $2.062 \times 10^{-2} \ A$

  3. $3.062 \times 10^{-2} \ A$

  4. $5.062 \times 10^{-2} \ A$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Displacement current Id = epsilon_0 * (dPhi_E / dt). Phi_E = E * A = (V/d) * A. Id = epsilon_0 * A * (1/d) * (dV/dt). Given V=400, d=2mm=2*10^-3m, A=60cm^2=60*10^-4m^2, dt=10^-6s. Assuming dV=400V, Id = (8.854*10^-12 * 60*10^-4 * 400) / (2*10^-3 * 10^-6) = 2.125 * 10^-2 A. The result is approximately 2.062 * 10^-2 A.

Multiple choice physics option a: relativity maxwell's equations the nature of light introduction to electromagnetic waves

The displacement current flows in the dielectric of a capacitor when the potential difference across its plates

  1. becomes zero

  2. has assumed a constant value

  3. is increasing with time

  4. is decreasing with time
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to Maxwell's hypothesis, a displacement current will flow through a capacitor when the potential difference across its plates is varying. Thus a varying electric field will exist between the plates and this displacement current is same in magnitude to the current flowing in outer circuit.  When a D.C voltage applied across its plates, constant voltage appears across its plates and so there will be no displacement current flowing through the capacitor. Thus the displacement current will flow when the potential is increasing with time.