Magnetism and Maxwell's Equations MCQ Quiz - Objective Question with Answer for Magnetism and Maxwell's Equations - Download Free PDF

Explanation:

The magnetic permeability (μ) of a material is related to its magnetic susceptibility (χ_m) as:

μ = μ₀(1 + χ_m)

Where:

• μ = magnetic permeability of the material
• μ₀ = permeability of free space (vacuum)
• χ_m = magnetic susceptibility of the material

This shows a linear relationship between magnetic susceptibility and magnetic permeability for most materials.

However, in many practical magnetic materials, when susceptibility increases significantly, effective permeability may appear to vary inversely in certain contexts like demagnetizing fields or in relative comparisons.

Correct relation: μ = μ₀(1 + χ_m) ⇒ linear relation

Calculation:

Without considering uncentainity in ℓ.

\(\mathrm{B}=\frac{\mu_{0}}{4 \pi} \frac{\mathrm{~m}}{\mathrm{r}^{3}}\)

\(\mathrm{B} \propto \frac{1}{\mathrm{r}^{3}}\)

\(\frac{\Delta \mathrm{B}}{\mathrm{~B}}=3 \times\left(\frac{\Delta \mathrm{r}}{\mathrm{r}}\right)\)

% uncertainity in B = 3%

Concept:

Lenz's Law: Lenz’s Law states that the induced current in a circuit always flows in such a direction that it opposes the change in magnetic flux that produced it.

• When a bar magnet moves towards the coil, the flux linked with the coil increases.
• To oppose this increase, the coil will generate a magnetic field opposite to that of the magnet.
• In this case, since the North (N) pole of the magnet is approaching, the coil will behave like a North pole on the side facing the magnet.
• Using the Right-Hand Rule, the direction of the induced current is determined.

Calculation:

Given,

The bar magnet moves towards the stationary coil with velocity v.

⇒ According to Lenz’s Law, the coil opposes the motion by acting as a North pole on the side facing the magnet.

⇒ For the observer on the Right-Hand Side (RHS), the current in the coil must flow clockwise to create a North pole.

∴ The direction of the induced current, as seen by the observer on the RHS, is clockwise.

Calculation:

ϕ = BAN.cos(ωt)

\(\varepsilon=\frac{-\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{BA} \omega \mathrm{N} . \sin (\omega \mathrm{t})\)

When B is parallel to plane, \(\underline{\underline{\omega}} \mathrm{t}=\frac{\pi}{2}\)

⇒ ϕ = 0, ε = BAωN

CONCEPT:

• Bar Magnet: A bar magnet consists of two equal and opposite magnetic pole separated by a small distance. Poles are not exactly at the ends.
• The shortest distance between two poles is called effective length (Le) and is less than its geometric length (Lg) for bar magnet.
• Magnetic field and magnetic lines of force: It is the space around a magnetic pole or magnet or current-carrying wire within which it's magnetic effect can be experienced is defined as a magnetic field.

• The magnetic field can be represented with the help of a set of lines or curves called magnetic lines of force.

EXPLANATION:

Properties of magnetic field line:

1. The magnetic field line is directed from the north pole to the south pole.
2. Magnetic field lines are closed and continuous.
3. Magnetic field lines are more crowded near poles.
4. Magnetic field lines never intersect with each other.

• Magnetic field lines originate from the north pole and terminate at the south pole while forming continuous closed paths. Therefore option 3 only satisfies this property.

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:

• Magnetic susceptibility (χm): It is the property of the substance which shows how easily a substance can be magnetized.
• It is defined as the ratio of the intensity of magnetization (I) in a substance to the magnetic intensity (H) applied to the substance,  i.e. \(\chi = \frac{I}{H}\)
• It is a scalar quantity with no units and dimensions. 

EXPLANATION:

• Paramagnetic substances are those which develop feeble magnetization in the direction of the magnetizing field.
• Such substances are feebly attracted by magnets and tend to move from weaker to stronger parts of a magnetic field.
• Magnetic susceptibility is small and positive i.e. 0 <  χ. Therefore option 1 is correct.
• Example: Manganese, aluminum, chromium, platinum, etc.

Diamagnetic substances:

• Diamagnetic substances are those which develop feeble magnetization in the opposite direction of the magnetizing field.
• Such substances are feebly repelled by magnets and tend to move from stronger to weaker parts of a magnetic field.
• Magnetic susceptibility is small and negative i.e. -1 ≤  χ ≤ 0. 
• Examples: Bismuth, copper, lead, zinc, etc.

Ferromagnetic substances:

• Ferromagnetic substances are those which develop strong magnetization in the direction of the magnetizing field.
• They are strongly attracted by a magnet and tend to move from weaker to the stronger part of a magnetic field.
• Magnetic susceptibility is very large and positive i.e. χ > 1000
• Example: Iron, cobalt, nickel, gadolinium, and alloys like alnico.

Key Points

• The neutral point in the magnetic field of a horizontally positioned bar magnet is the point where the magnetic field is zero.
• This point is also known as the magnetic equator or the magnetic neutral axis.
• At this point, the magnetic field lines of the magnet are parallel to the surface of the earth.
• The location of the neutral point depends on the strength and orientation of the magnet.

Additional Information

• Magnetic field does not change direction at the neutral point, but rather it changes direction at the poles of the magnet.
• Magnetic field is not necessarily the weakest at the neutral point, as it can be weaker or stronger depending on the distance from the magnet and the strength of the magnet.
• Magnetic field is strongest at the poles of the magnet.

Concept:

• Diamagnetic Substances are substances that acquire feeble magnetism when placed in a magnetic field and the direction of the induced magnetic field is opposite to that of the applied magnetic field. Examples are bismuth, copper, silver, gold, mercury etc. 
• Paramagnetic Substances are substances that acquire feeble magnetism when placed in a magnetic field and the direction of the induced magnetic field is the same as that of the applied magnetic field. Examples are aluminium, manganese, platinum etc. 
• Ferromagnetic substances are substances that acquire strong magnetism when placed in a magnetic field and the direction of the induced magnetic field is same as that of the applied magnetic field. Examples are iron, cobalt, nickel etc. 
• Ferrimagnetic Substances: This effect is observed when the magnetic moments of the domains in the substance are aligned in parallel and anti-parallel directions in unequal numbers. Ferrimagnetic substances are weakly attracted by a magnetic field as compared to ferromagnetic substances. Example: NiFe2O4, CoFe2O4, Fe3O4 (or FeO.Fe2O3), CuFe2O4 etc.

Explanation:

• Ferromagnetic metals are strongly attracted by a magnetic force.
• The common ferromagnetic metals include iron, nickel, cobalt and alloys such as steel.
• Ferromagnetic metals are commonly used to make permanent magnets.

CONCEPT:

• Magnet: A magnet is an object that has a magnetic field. A magnet attracts or repels other magnets or magnetic materials.
  • When two magnets are brought together, the opposite poles will attract one another, but the like poles will repel one another. 
• A natural magnet is nothing but an ore of iron that attracts small pieces of iron, nickel, and cobalt towards it.

EXPLANATION:

• The magnetite of Lodestone is an example of Natural magnets. 

Additional Information

• Bar magnet, Horseshoe magnet & Electromagnet are examples of the artificial magnet. 

CONCEPT:

• The magnitude of the internal polarization (J) divided by the strength of the external field (B) is called Magnetic susceptibility.
• It is denoted by Greek letter chi (χ).
• Based on magnetic property materials are of 4 types:

1. Diamagnetic
2. Paramagnetic
3. Superparamagnetic
4. Ferromagnetic

EXPLANATION:

• Below table shows Magnetic Susceptibility χ for different materials:
   

• Given that magnetic material is 400.
• This is a higher value. Comparing to the values in the table the material will be Ferromagnetic.
• So, the answer will be option 3.

Important Points

The susceptibility of ferromagnetic material is Large and positive. Ferromagnetic materials follow the Curie – Weiss law. When ferromagnetic substance heated above Curie temperature (T_c)

\(i.e.\chi \propto \frac{1}{{T - {T_C}}}\)

Concept:

Magnet: It is defined as a material that can produce its own magnetic field. There are two types of magnet,

• Permanent magnet
• Temporary magnet

Permanent magnet: These magnets do not lose their magnetic property once they are magnetized. For example alnico, samarium cobalt, ferrite.

Temporary magnet: These magnets act like permanent magnets only when they are within a strong magnetic field. It is made up of soft iron. for example electromagnet.

Alnico:

• The alloy which are permanent magnets that are primarily made up of a combination of aluminium, nickel and cobalt but can also include copper, iron and titanium.
• It can be easily magnetized in an external magnetic field.
• Due to its high coercivity and low retentivity, ​it will not lose its magnetic property.
• It has excellent temperature stability.

Explanation:

• Aluminum behaves like a very weak magnet. When exposed to permanent magnets, paramagnetic materials are weakly attracted.
• Soft iron does not retain magnetism permanently, therefore soft iron core is used in electromagnets.
• Copper is not magnetic itself. We can't observe it without very large magnetic fields.

From the above discussion, we can conclude that alnico is the best material to make a permanent magnet.

The correct answer is North pole to South pole. 

Key Points

CONCEPT:

• Magnet: A magnet is an object that has a magnetic field. A magnet attracts or repels other items.
  • Like magnetic poles (N-N and S-S) repel each other and unlike magnetic (N-S) poles attract each other.
• Magnetic field lines: Magnetic field strength is shown with the help of magnetic field lines also known as magnetic lines of force.
• And as we can see magnetic field strength of any bar magnet is more at the poles compared to its center and this also true for any other magnetic material. 

EXPLANATION:

• The direction of magnetic field lines outside a magnet is from the North Pole to the South Pole. So option 3 is correct.
• This is because the North and South Poles of a magnet attract each other due to the position and motion of electric charges.

The correct answer is option 3) i.e. Convection currents in Earth's core

CONCEPT:

• The magnetic field of Earth: The Earth behaves like a huge bar magnet with two poles that are located along the ends of Earth's diameter.
  • The core of the Earth contains molten metal - iron and nickel.​
  • The flowing molten material moves the charges and generates an electric current.
  • The rotation of Earth about its axis produces a magnetic field around it.

EXPLANATION:

• The Earth has its magnetic field obtained from the flow of hot metal core i.e. convective currents in the Earth's core.