QUE 1>
A> (i) Coulomb’s Law is an electrostatic law that states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It is given by the formula:
F = kq1q2/r2
where F =force, k =Coulomb’s constant, q1 and q2=two point charges r= distance between them.
(ii) Relative permeability is a dimensionless quantity that represents the ability of a material to conduct magnetic flux compared to that of free space. It is given by the formula:
μr = μ/μ0
where μ=the permeability of the material
μ0=is the permeability of free space.
B> Superconductivity is a phenomenon where certain materials exhibit zero electrical resistance and expel magnetic fields when cooled below a critical temperature.
The important parameters to achieve the superconducting state in a material include:
- Critical temperature (Tc) – It is the temperature below which a material exhibits superconductivity.
- Critical magnetic field (Hc) – It is the maximum magnetic field that a superconductor can withstand before losing its superconductivity.
- Critical current density (Jc) – It is the maximum current density that a superconductor can carry without losing its superconductivity.
- Type of superconductors – There are two types of superconductors, type-I and type-II, which have different properties and applications.
C>
| MUSICAL SOUND | NOISE |
| Musical sound refers to a sound that is harmonious, organized and has a definite pitch | Noise refers to an unpleasant, chaotic and random sound. |
| Musical sounds have a well-defined and consistent frequency content, | noise has an irregular frequency content. |
| Musical sounds are usually composed of a few frequencies that are related to each other in a harmonic way | noise contains a wide range of frequencies that are not related to each other. |
| Musical sounds are usually perceived as pleasant and enjoyable | noise is generally considered unpleasant and annoying. |
QUE 2>
A> A dielectric material is an insulating material that can store and transmit electrical energy by polarization of its atoms or molecules. It is placed between the plates of a capacitor to increase its capacitance by reducing the electric field between the plates.
Given, the separation between the plates of the capacitor, d = 6.0 mm = 6.0 × 10^−3 m The dielectric constant of the material, K = 2.8 The electric field strength inside the capacitor, E = 103 V/m (Note: the unit is V/m, not 10° V/m)
The polarization vector, P can be calculated using the equation: P = ε0 (K-1) E
where, ε0 is the permittivity of free space (8.85 × 10-12 F/m)
Substituting the values, we get:
P = (8.85 × 10-12 F/m) × (2.8-1) × 103 V/m P
= 1.9836 × 10-8 C/m^2
The displacement vector, D can be calculated using the equation: D = εoE + P
Substituting the values, we get:
D = (8.85 × 10-12 F/m) × 103 V/m + 1.9836 × 10-8 C/m^2 D
= 8.85 × 10-9 C/m^2 + 1.9836 × 10-8 C/m^2 D
= 2.8724 × 10-8 C/m^2
Therefore, the polarization vector is 1.9836 × 10-8 C/m^2 and the displacement vector is 2.8724 × 10-8 C/m^2.
Que 2>
A> A magnetic material is a material that can be magnetized or attracted by a magnetic field. The ability of a material to be magnetized depends on its atomic structure and the arrangement of electrons.
Given, Magnetization (M) = 3400 A/m
Magnetic induction (B) = 0.006
T Thickness of material (d) = 1 m (considering unit cross-sectional area)
Permeability of free space (μ0) = 4π × 10-7 H/m
The magnetizing field (H)
H = B/μ0 = 0.006/4π × 10-7
= 477.46 A/m
The magnetic susceptibility (χ)
χ = M/H = 3400/477.46
= 7.12
The relative permeability (μr)
μr = 1 + χ
= 1 + 7.12
= 8.12
Therefore, the magnetizing field is 477.46 A/m, the magnetic susceptibility is 7.12, and the relative permeability is 8.12.
B> 1.Room shape and size: The shape and size of the room greatly affect its acoustic properties. A rectangular room with non-parallel walls and ceiling is preferred.
2.Materials used in construction: The materials used in construction, such as walls, ceilings, and floors, greatly affect the acoustics. Hard surfaces reflect sound while soft surfaces absorb it.
3.Sound isolation: Good acoustic design also includes sound isolation, which prevents sound from outside the room from entering and sound from inside the room from leaking out.
4.Sound reinforcement: The use of sound reinforcement systems, such as speakers and microphones, is important to ensure that sound is evenly distributed throughout the room.
5.HVAC systems: Proper design of heating, ventilation, and air conditioning (HVAC) systems can greatly affect the acoustics of a room by controlling ambient noise levels and ensuring proper air flow.
B> Quartz crystal is a piezoelectric material that generates an electrical signal when mechanically stressed. This property of quartz crystal is utilized to generate ultrasonic waves. An oscillator circuit is used to apply a high-frequency electrical signal to the quartz crystal, which in turn generates mechanical vibrations at the same frequency. These mechanical vibrations are then transmitted through a transducer to generate ultrasonic waves. The transducer is designed in such a way that it amplifies and directs the ultrasonic waves in a specific direction. The diagram below shows the basic setup for generating ultrasonic waves using a quartz crystal.
QUE 3>
A> 1.Electronic polarization: This occurs in all dielectrics and is due to the displacement of the electron cloud within each atom or molecule. The resulting electric dipole moment is proportional to the strength of the external electric field.
2.Ionic polarization: This occurs in materials that contain ions. The ions are displaced in the presence of an external electric field, resulting in the formation of an electric dipole moment.
3.Orientation polarization: This occurs in polar molecules that have permanent dipole moments. When an external electric field is applied, the polar molecules align themselves with the electric field.
4.Space charge polarization: This occurs in materials that have mobile charges such as ions or electrons. The external electric field causes these charges to move and accumulate at the boundaries of the material, resulting in a net polarization.
Que 3>
A> The critical magnetic field, also known as the upper critical field, is the maximum external magnetic field that can be applied to a superconductor before it loses its superconductivity.
To find the transition temperature of niobium, we can use the Werthamer-Helfand-Hohenberg (WHH) theory which relates the critical field to the transition temperature:
Bc2(T) = Bc2(0)[1 – (T/Tc)^2]/[1 + (T/Tc)^2]
where Bc2(T) is the critical magnetic field at temperature T, Bc2(0) is the critical magnetic field at absolute zero temperature, and Tc is the transition temperature.
Using the given values, we can solve for Tc:
1 X 10^5 = Bc2(0)[1 – (8/Tc)^2]/[1 + (8/Tc)^2] 2 X 10^5 = Bc2(0)[1 – (0/Tc)^2]/[1 + (0/Tc)^2]
Dividing the second equation by the first, we get:
2 = [1 – (0/Tc)2]/[1 + (0/Tc)2] x [1 + (8/Tc)2 ][1 – (8/Tc)2]
Simplifying and solving for Tc, we get:
Tc = 9.17 K
Therefore, the transition temperature of niobium is approximately 9.17 K.
B> Hysteresis loss is the energy lost due to the reversal of magnetization in a magnetic material, as it goes through a complete cycle of magnetization and demagnetization. The hysteresis loop is a graphical representation of the magnetic behavior of a material as it is magnetized and demagnetized.
The hysteresis loop consists of two parts: the magnetization curve and the demagnetization curve. The magnetization curve shows how the material magnetizes when an increasing magnetic field is applied, while the demagnetization curve shows how the material demagnetizes when the magnetic field is reduced.
The retentivity (Br) of a magnetic material is the residual magnetization remaining in the material after the magnetic field has been removed. It is represented on the hysteresis loop as the point where the demagnetization curve intersects the y-axis.
The coercivity (Hc) of a magnetic material is the amount of magnetic field required to demagnetize the material. It is represented on the hysteresis loop as the point where the magnetization curve intersects the x-axis.
The area enclosed by the hysteresis loop represents the energy lost as heat due to the reversal of magnetization, which is known as hysteresis loss. The amount of hysteresis loss depends on the size and shape of the hysteresis loop, which in turn depends on the magnetic properties of the material.
C>1. Medical imaging: Ultrasound is commonly used for diagnostic imaging to visualize internal organs, tissues, and blood flow.
2.Non-destructive testing: Ultrasound is used to inspect and evaluate the quality of materials and structures, such as metals, plastics, and concrete.
3.Cleaning: Ultrasonic cleaners use high-frequency sound waves to remove dirt and contaminants from delicate objects.
4.Welding and cutting: Ultrasound can be used to join and cut materials, such as plastics, metals, and ceramics.
5.Sonar and navigation: SONAR (Sound Navigation and Ranging) uses ultrasound to determine the depth and location of objects underwater.
SONAR technology is commonly used for mapping the seafloor, detecting underwater objects such as submarines or shipwrecks, and studying marine life.