Displacement Current MCQ Quiz - Objective Question with Answer for Displacement Current - Download Free PDF

The correct answer is: Option 2) ε₀ dΦₑ / dt

Concepts:

Displacement current is a concept introduced by James Clerk Maxwell to account for the apparent current in regions where there is a time-varying electric field but no actual movement of charge carriers.

The displacement current density (J_d) is given by the equation:

J_d = ε₀ (dE / dt)

where ε₀ is the permittivity of free space and dE/dt is the rate of change of the electric field with respect to time.

When considering the entire surface, the displacement current (I_d) can be written as:

I_d = ε₀ (dΦₑ / dt)

where Φₑ is the electric flux.

Calculation:

Given that the displacement current due to a time-varying electric field is needed, we use the formula:

I_d = ε₀ (dΦₑ / dt)

This directly corresponds to Option 2.

Calculation:

A magnetic material loses its magnetic property when it is heated to high temperature. This is because when a magnetic material is heated above a certain temperature, the thermal energy disrupts the alignment of its magnetic domains, causing it to lose its magnetism.

The correct answer is option 4: Heated to high temperature.

Answer : 2

Solution :

The correct relation according to Curie's Law in magnetism is:

Option 2 M = 

Curie's Law states that the magnetization M of a paramagnetic material is directly proportional to the applied magnetic field B, and inversely proportional to the absolute temperature T of the material. The proportionality constant C is known as the Curie constant and is specific to the paramagnetic material.

To better understand this law, let's dissect Option 2, which correctly reflects the Curie's Law formula. The Magnetization M, which is the extent to which the material becomes magnetized when exposed to an external magnetic field, is given by:

M =

- C is the Curie constant,

- B is the applied magnetic field, and

- T is the absolute temperature.

So, the higher the field B, the larger the induced magnetization M, and the higher the temperature T, the smaller the magnetization due to the increased thermal motion of the magnetic moments which tend to randomize the orientation and reduce magnetization. The correct formula (Option 2) reflects this inverse temperature dependence and direct magnetic field dependence of the magnetization.

The Correct answer is Both Statement-I and Statement-II are true.

Key Points

• Statement I: Susceptibilities of paramagnetic and ferromagnetic substances increase with a decrease in temperature.
  • ​This is correct for both paramagnetic and ferromagnetic materials. According to Curie’s Law for paramagnetic substances, the magnetic susceptibility is inversely proportional to the temperature
  • For ferromagnetic substances, as temperature decreases, magnetic domains become more aligned, and susceptibility increases.
  • However, if the temperature exceeds Curie temperature, ferromagnetic substances lose their ferromagnetism and behave like paramagnetic materials.
• Statement-II: Diamagnetism results from orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.
  • ​ This is also correct.
  • Diamagnetism occurs due to the induced magnetic moment in the material when an external magnetic field is applied.
  • The electrons in orbitals adjust their motion such that the induced magnetic moments are in the direction opposite to the applied field, causing a repulsive effect.

CONCEPT:

• Curie temperature: Curie temperature is the temperature at which the magnetic properties of a material change.
  • When the temperature is greater than the Curie temperature, ferromagnetic material becomes paramagnetic material.

• Ferromagnetic material: Ferromagnetic materials have a large, positive susceptibility to an external magnetic field. They exhibit a strong attraction to magnetic fields and can retain their magnetic properties after the external field has been removed. For examples Iron, nickel, and cobalt.
• Paramagnetic material: Paramagnetic materials have a small, positive susceptibility to magnetic fields. These materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed. For examples magnesium, molybdenum, lithium.

EXPLANATION:

• Curie temperature is the temperature at which the magnetic properties of a material change. When the temperature is greater than Curie temperature, ferromagnetic material becomes paramagnetic material.

So option 3 is correct.

CONCEPT:

• Curie temperature: Curie temperature is the temperature at which the magnetic properties of a material change. At this temperature, the magnetic materials lose their magnetic property.
  • When the temperature is greater than the Curie temperature, ferromagnetic material becomes paramagnetic material.

• Diamagnetic Substance: Diamagnetic substances are those which develop feeble magnetization in the opposite direction of the magnetizing field.

• Paramagnetic substances: Paramagnetic substances are those which develop feeble magnetization in the direction of the magnetizing field.

• Ferromagnetic substances: Ferromagnetic substances are those which develop strong magnetization in the direction of the magnetizing field.

EXPLANATION:

• The minimum temperature at which a ferromagnetic substance is converted into a paramagnetic substance is defined as Curie temperature.
• At this temperature, the ferromagnetism of the substances suddenly vanishes.

When ferromagnetic material heated beyond curie temperature,  turns into paramagnetic material, as the ferromagnetic domains become random.

Curie temperature:

Curie temperature is the temperature at which the magnetic properties of a material change.

When the temperature is greater than the Curie temperature, ferromagnetic material becomes paramagnetic material. Here, X as (magnetic susceptibility) vs. T (temperature)

Additional Information

Ferromagnetism:

Ferromagnetism is the presence of magnetic domains which are aligned in the same direction in magnetic materials. The most common examples of ferromagnetic materials are metals such as iron, nickel, cobalt, and metal alloys.

Antiferromagnetism:

• Antiferromagnetism is the presence of magnetic domains that are aligned in opposite directions in magnetic materials.
• These opposite magnetic domains have equal magnetic moments which are canceled out (since they are in opposite directions).
• This makes the net moment of material zero. This type of material is known as antiferromagnetic materials.

Classification of magnetic materials:

CONCEPT:

Ferromagnetic materials:

• In some materials, the permanent atomic magnetic moments have a strong tendency to align themselves even without any external field.
• These materials are called ferromagnetic materials.
• In every unmagnetized ferromagnetic material, the atoms form domains inside the material.
• Different domains, however, have different directions of magnetic moment and hence the materials remain unmagnetized.
• On applying an external magnetic field, these domains rotate and align in the direction of the magnetic field.

EXPLANATION:

• Beyond curie temperature, ferromagnetic material turns into paramagnetic material, as if ferromagnetic domains become random. Therefore option 1 is correct.

CONCEPT:

• Curie temperature (T_c): The minimum temperature at which a ferromagnetic substance is converted into paramagnetic substance is defined as Curie temperature.
• The temperature above which a ferromagnetic material behaves like a paramagnetic material is defined as Curie temperature.
• At this temperature, the ferromagnetism of the substances suddenly vanishes.

EXPLANATION:

• From above it is clear that curie temperature is the temperature above which a ferromagnetic material becomes paramagnetic. Thus option2 is correct.

Explanation:

Curie temperature:

• It is the temperature above which ferromagnetic materials lose their permanent magnetic field and the magnetism completely disappears.
• The magnetic susceptibility decreases with an increase in temperature. So, the ferromagnetism decreases with rising temperature. It is maximum at absolute zero temperature and becomes zero at Curie temperature. Above this temperature, the ferromagnetic material behaves as a paramagnetic substance.

• The Curie temperature of some of the materials is:

Iron (Fe) = 1043 K

Cobalt (Co) = 1400 K

Nickel (Ni) = 627 K

option(1)

CONCEPT:

• Curie Temperature: It is that Curie point, at which above this temperature certain materials lose their permanent magnetic properties.
• Curie is the temperature of electricity at which a change in the magnetic properties of the metal happens.

EXPLANATION:

• Curie Temperature: It is also known as Curie point, which is the temperature at which certain magnetic materials undergo a sharp change in their magnetic properties.

Mat hematically it can be represented as:

M =C × (B/T)  where C is the spe cific curie constant, B is the magnetic field and T is the absolute temperature.

The concept of displacement current was proposed by Maxwell

CONCEPT:

Displacement current (ID): 

• It is that current that comes into existence, in addition to the conduction current, whenever the electric field and hence the electric flux changes with time
• To modify Ampere’s law, Maxwell followed a symmetry consideration.
• By Faraday’s law, a changing magnetic field induces an electric field, hence a changing electric field must induce a magnetic field.
• As currents are the usual sources of the magnetic field, a changing electric field must be associated with the current.
• Maxwell called that current as displacement current.
• To maintain the dimensional consistency, the displacement current is added in ampere’s law: 

Where,  is the displacement current.

EXPLANATION:

• From the above, it is clear that the concept of displacement current was proposed by Maxwell. Therefore option 4 is correct. 

Concept:

Susceptibility is given by

Where χ_m = Susceptibility of material

C = curie constant

θ = Curie temperature

This expression is valid for T > θ and this expression is called curie Weiss law.

Calculation:

Given C = 0.2

T - θ = 0.01

Correct option-1

CONCEPT:

Displacement current: 

• It is that current that comes into existence, in addition to the conduction current, whenever the electric field and hence the electric flux changes with time

• The is the rate of change of the electric flux through a closed loop. Apart from conduction current, the displacement current does not appear from the real movement of electric charge as is the case for conduction current.
• The expression for displacement current is given by

Where ϕE = The flux of the electric field through the area bounded by the closed curve, id =  Displacement current, and ϵo = Permittivity of free space

The idea of displacement current was firstly developed by famous physicist James Maxwell. 

• The SI unit of Displacement current is Ampere.  
• The magnitude of Displacement current is Zero in the case of steady electric fields in conducting wire.
• The idea of Displacement current was introduced to the current for making ampere circuital law consistent.

CALCULATION:

Given: Capacitance (C) = 1 μF, Rate of change in voltage,  

• The expression for displacement current i_d, in the case of capacitance is given as-

    ....(i)

• As we also know that, the charge on the capacitor is 

⇒ q = CV

Where q = charge on the capacitors

On substitute the value of q = CV in equation (i), we get

    ...(ii)

On substituting the given values in equation (ii), we get

⇒ i_d = 1 A

• Hence, Option-1 is correct.