Electromagnetic Theory MCQ Quiz - Objective Question with Answer for Electromagnetic Theory - Download Free PDF

Concept:

The characteristic impedance $Z_0$ of a lossless transmission line is given by:

$Z_0=\sqrt{\frac{L}{C}}$

Where,

• $L$ = Inductance per unit length (in H/m)
• $C$ = Capacitance per unit length (in F/m)

Given:

$L=100\text{nH/m}=100\times {10}^{-9}\text{H/m}$

$C=40\text{pF/m}=40\times {10}^{-12}\text{F/m}$

Calculation:

$Z_0=\sqrt{\frac{100\times {10}^{-9}}{40\times {10}^{-12}}}=\sqrt{\frac{100}{40}\times {10}^3}=\sqrt{2.5\times {10}^3}=\sqrt{2500}=50\mathrm{\Omega }$

Hence, the correct answer is 3

The VSWR is mathematically related to the reflection coefficient (Γ), which quantifies the fraction of incident power reflected back due to impedance mismatch between the transmission line and the load. The reflection coefficient is given by:

Γ = (VSWR - 1) / (VSWR + 1)

Given in the problem:

• VSWR = 1.5
• Incident power = 50 W

Step 1: Calculate the Reflection Coefficient (Γ):

Substitute the given VSWR value into the formula:

Γ = (1.5 - 1) / (1.5 + 1)

Γ = 0.5 / 2.5

Γ = 0.2

Step 2: Calculate the Reflected Power:

The reflected power (P_reflected) can be calculated using the relation:

P_reflected = Γ² × P_incident

Substitute the values:

P_reflected = (0.2)² × 50

P_reflected = 0.04 × 50

P_reflected = 2 W

Correct Answer:

The reflected power is 2 W, which corresponds to Option 2.

Force Acting on Two Parallel Current-Carrying Conductors

Definition: When two parallel current-carrying conductors are placed near each other, they exert a force on each other due to the interaction of their magnetic fields. The direction and nature of this force depend on the direction of the currents in the two conductors. If the currents flow in the same direction, the force is attractive, and if the currents flow in opposite directions, the force is repulsive.

Working Principle:

The phenomenon can be explained using Ampere's law and the Biot-Savart law:

• Each conductor generates a magnetic field around it due to the flow of current. The magnetic field produced by a current-carrying conductor at a distance r from it is given by:

B = (μ₀ × I) / (2π × r)

• Here, B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the conductor.
• The second conductor, placed in the magnetic field of the first conductor, experiences a force due to the magnetic field. This force is given by:

F = I × L × B

• Here, F is the force, L is the length of the conductor, and B is the magnetic field.

Substituting the value of B into the formula for force:

F = (μ₀ × I₁ × I₂ × L) / (2π × r)

• Here, I₁ and I₂ are the currents in the two conductors, and r is the distance between them.

The direction of the force can be determined using the right-hand rule. If the currents in the two conductors are in the same direction, the force is attractive. If the currents are in opposite directions, the force is repulsive.

Correct Option Analysis:

The correct option is:

Option 4: Attractive

When the currents in the two parallel conductors flow in the same direction, the magnetic fields around the conductors interact in such a way that the conductors attract each other. This phenomenon is a direct consequence of the magnetic field interaction and is consistent with the principles of electromagnetism.

The force of attraction can be calculated using the formula:

F = (μ₀ × I₁ × I₂ × L) / (2π × r)

• Here, F is the attractive force per unit length of the conductors.
• μ₀ is the permeability of free space (4π × 10⁻⁷ H/m).
• I₁ and I₂ are the currents in the two conductors.
• L is the length of the conductors.
• r is the distance between the conductors.

This formula highlights that the force is proportional to the product of the currents and inversely proportional to the distance between the conductors.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Zero

This option is incorrect because the force is not zero. The magnetic fields produced by the currents interact with each other, resulting in a force between the conductors. The force can only be zero if the currents are zero or the conductors are infinitely far apart, which is not the case here.

Option 2: Infinite

This option is incorrect because the force cannot be infinite. The force depends on the currents, the distance between the conductors, and the permeability of free space, all of which are finite quantities under normal circumstances.

Option 3: Repulsive

This option is incorrect because the force is repulsive only when the currents in the two conductors flow in opposite directions. In this case, since the currents are in the same direction, the force is attractive.

Option 5: (No Option Provided)

This option is not valid because it does not contain any relevant information or alternative explanation for the phenomenon.

Conclusion:

The force acting on two parallel current-carrying conductors is attractive if the currents flow in the same direction. This attractive force arises from the interaction of the magnetic fields generated by the currents in the conductors. Understanding this concept is essential for applications in electromagnetism, such as in the design of electrical machines and power transmission systems.

Explanation:

Ohm's Law for Magnetic Circuits:

Definition: Ohm's law for a magnetic circuit states that the magnetomotive force (MMF) is equal to the product of the magnetic flux and the magnetic reluctance. This relationship is analogous to Ohm's law in electrical circuits, where the voltage is equal to the product of current and resistance.

Mathematical Representation:

The equation for Ohm's law in a magnetic circuit is:

MMF = Φ × R

• MMF: Magnetomotive force, measured in ampere-turns (At).
• Φ: Magnetic flux, measured in webers (Wb).
• R: Magnetic reluctance, measured in ampere-turns per weber (At/Wb).

Correct Option Analysis:

The correct option is:

Option 3: Magnetomotive force to magnetic reluctance.

This option correctly represents the relationship defined by Ohm's law for magnetic circuits. The magnetomotive force (MMF) is the driving force that creates magnetic flux in a magnetic circuit. When divided by the magnetic reluctance, it gives the magnetic flux, which is analogous to the current in an electrical circuit. Therefore, MMF is proportional to the product of magnetic flux and magnetic reluctance, aligning with the principles of Ohm's law.

Detailed Explanation:

In magnetic circuits, just as in electrical circuits, there is a driving force, a flow, and opposition to flow. These terms correspond to:

• Driving Force: Magnetomotive force (MMF), analogous to voltage in electrical circuits.
• Flow: Magnetic flux (Φ), analogous to current in electrical circuits.
• Opposition: Magnetic reluctance (R), analogous to resistance in electrical circuits.

When MMF is applied across a magnetic circuit, it generates magnetic flux, which flows through the circuit. The opposition to this flow is provided by the magnetic reluctance, which depends on factors like the material's permeability, cross-sectional area, and length of the magnetic path.

The analogy to Ohm's law in electrical circuits makes it easier to understand and analyze magnetic circuits using similar principles. In this context:

• MMF: Represented as the product of current (I) and the number of turns (N) in the coil, i.e., MMF = N × I.
• Magnetic Flux: The quantity of magnetic field passing through a given area, denoted as Φ.
• Magnetic Reluctance: The opposition to the formation of magnetic flux, calculated using the formula R = l/(μ × A), where:
  • l: Length of the magnetic path.
  • μ: Permeability of the material.
  • A: Cross-sectional area of the magnetic path.

Thus, the correct option, "Magnetomotive force to magnetic reluctance," aligns with the established relationship in magnetic circuits.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Magnetic reluctance to magnetic flux.

This option is incorrect because it misrepresents the relationship defined by Ohm's law. Magnetic reluctance is the opposition to magnetic flux, and its ratio to magnetic flux does not define MMF. Instead, MMF is the product of flux and reluctance, as established by the law.

Option 2: Magnetic reluctance to magnetomotive force.

This option is incorrect as well because it inverses the relationship. Magnetic reluctance, when divided by MMF, does not yield a meaningful physical quantity in the context of Ohm's law for magnetic circuits. The flux is obtained by dividing MMF by reluctance, not the other way around.

Option 4: Magnetomotive force to permeance.

This option is partially misleading. Permeance is the reciprocal of reluctance and represents the ease with which magnetic flux can be established in a material. While MMF divided by permeance equals magnetic flux, this option is not the most direct representation of Ohm's law for magnetic circuits, which specifically uses reluctance as the term for opposition.

Conclusion:

Understanding the principles of Ohm's law for magnetic circuits is essential for analyzing magnetic systems. The correct option, "Magnetomotive force to magnetic reluctance," accurately describes the fundamental relationship in such circuits, where MMF drives magnetic flux through a material, overcoming the opposition of magnetic reluctance.

Explanation:

Inductance of a Coil

Definition: Inductance is a property of a coil or inductor that determines how effectively it can store energy in the form of a magnetic field when an electric current flows through it. It is denoted by the symbol ‘L’ and measured in henries (H). The inductance of a coil depends on various factors, including the number of turns in the coil, its geometry, and the material inside or surrounding the coil.

Impact of Placing an Iron Bar Inside the Coil:

When an iron bar is placed inside a coil, the inductance of the coil increases. This phenomenon occurs due to the high magnetic permeability of iron. Magnetic permeability is a measure of how easily a material can support the formation of a magnetic field within itself. Iron has a much higher magnetic permeability compared to air or vacuum, which means it can concentrate magnetic field lines more effectively.

Explanation:

The inductance of a coil is given by the formula:

L = μ × N² × A / l

• μ: Magnetic permeability of the core material (iron, air, etc.)
• N: Number of turns in the coil
• A: Cross-sectional area of the coil
• l: Length of the coil

From the above formula, it is evident that the inductance is directly proportional to the magnetic permeability (μ) of the core material inside the coil. When an iron bar is inserted into the coil, the magnetic permeability of the core increases significantly compared to air, resulting in a larger inductance value.

Iron, being ferromagnetic, enhances the magnetic field within the coil. This increased magnetic field leads to a higher inductance because the coil can now store more magnetic energy for the same amount of current flowing through it. This principle is widely utilized in the design of inductors and transformers where iron cores are used to achieve high inductance values.

Practical Applications:

• Transformers: Iron cores are used in transformers to increase inductance and efficiency.
• Electromagnets: Iron cores enhance the magnetic field strength of electromagnets.
• Inductors: Iron cores are used in inductors to store magnetic energy effectively.

Correct Option Analysis:

The correct option is:

Option 2: Increases

When an iron bar is placed inside a coil, the inductance of the coil increases due to the higher magnetic permeability of iron. This allows the coil to store more magnetic energy, making this option the correct answer.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: Reduces to zero

This option is incorrect because placing an iron bar inside a coil does not reduce the inductance to zero. Iron, being a material with high magnetic permeability, increases the inductance rather than reducing it. Reducing inductance to zero would require a material that completely eliminates the magnetic field, which is not the case with iron.

Option 3: Remains unchanged

This option is incorrect because the inductance of a coil changes when an iron bar is placed inside it. The high magnetic permeability of iron enhances the magnetic field, causing the inductance to increase. Therefore, the inductance does not remain unchanged.

Option 4: Decreases

This option is incorrect because placing an iron bar inside a coil does not decrease the inductance. Instead, the inductance increases due to the improved ability of the iron core to concentrate magnetic field lines. Materials with lower magnetic permeability than air would be required to decrease the inductance, but iron does not fit this criterion.

Conclusion:

Understanding the behavior of inductance in the presence of different core materials is essential for designing electrical components like inductors and transformers. When an iron bar is placed inside a coil, the inductance increases due to the high magnetic permeability of iron. This principle is widely utilized in engineering applications to enhance the efficiency and functionality of electromagnetic devices.

Concept:

Electric Flux:

• It is defined as the number of electric field lines associated with an area element.
• Electric flux is a scalar quantity, because it's the dot product of two vector quantities, electric field and the perpendicular differential area.
   ϕ = E.A = EA cosθ 
• The SI unit of the electric flux is N-m2/C.

Electric flux density (D) is a vector quantity because it is simply the product of the vector quantity electric field and the scalar quantity permittivity of the medium, i.e.

$\stackrel{\rightharpoonup }{D}=\epsilon \stackrel{\rightharpoonup }{E}$

Its unit is Coulomb per square meter.

CONCEPT:

• Magnetic field strength or magnetic field induction or flux density of the magnetic field is equal to the force experienced by a unit positive charge moving with unit velocity in a direction perpendicular to the magnetic field.
  • The SI unit of the magnetic field (B) is weber/meter2 (Wbm-2) or tesla.
• The CGS unit of B is gauss.

​1 gauss = 10-4 tesla.

EXPLANATION:

• From the above explanation, we can see that the relation between tesla and Weber/m2 is given by:

1 tesla = 1 Weber/m2

CONCEPT:

• Fleming's Left-hand rule gives the force experienced by a charged particle moving in a magnetic field or a current-carrying wire placed in a magnetic field.
• It states that "stretch the thumb, the forefinger, and the central finger of the left hand so that they are mutually perpendicular to each other.
• If the forefinger points in the direction of the magnetic field, the central finger points in the direction of motion of charge, then the thumb points in the direction of force experienced by positively charged particles."

EXPLANATION:

• According to question

1. Forefinger (Index finger): Represents the direction of the magnetic field (magnetic flux). Therefore option 3 is correct.
2. Middle finger: Represents the direction of motion of charge (current).
3. The thumb : Represents the direction of force or motion experienced by positively charged particles.

Concept:

Coulomb's law: 

It states that the magnitude of the electrostatic force F between two point charges q1 and q2 is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance r between them. 

• It is represented mathematically by the equation:

$F=\frac{1}{4\pi {ϵ}_0}\frac{q_1{q}_2}{r^2}$

Where ϵ0 is the permittivity of free space (8.854 × 10-12 C2 N-1 m-2).

The value of $k=\frac{1}{4\pi {ϵ}_0}=9\times {10}^{9}N{m}^2{C}^{-2}$

Calculation:

So, initial the force between two charges q1 and q2 is 200 N. 

$F=k\frac{q_1{q}_2}{r^2}=200N$ -- (1)

If new distance r' = 2 r

New Force is

$F^{\prime }=k\frac{q_1{q}_2}{r^{\prime 2}}=k\frac{q_1{q}_2}{(2r{)}^2}$

$⟹F^{\prime }=k\frac{q_1{q}_2}{4r^2}=\frac{1}{4}k\frac{q_1{q}_2}{(r{)}^2}$     ---(2)

From (1) and (2)

$⟹F^{\prime }=\frac{F}{4}$

or

$⟹F^{\prime }=\frac{200N}{4}=50N$

So, the correct option is 50 N.

Concept:

Magnetic Field Strength (H): the amount of magnetizing force required to create a certain field density in certain magnetic material per unit length.

$H=\frac{NI}{L}$

The intensity of Magnetization (I): It is induced pole strength developed per unit area inside the magnetic material.

The net Magnetic Field Density (Bnet) inside the magnetic material is due to:

• Internal factor (I)
• External factor (H)
   

∴ Bnet ∝  (H + I)

Bnet = μ0(H + I) …. (1)

Where μ0 is absolute permeability.

Note: More external factor (H) causes more internal factor (I).

∴ I ∝  H

I = KH …. (2)

And K is the susceptibility of magnetic material.

From equation (1) and equation (2):

Bnet = μ0(H + KH)

Bnet = μ0H(1 + K) …. (3)

Dividing equation (3) by H on both side

$\frac{B_{net}}{H}=\frac{{\mu }_{0}H\left(1+K\right)}{H}$

or, μ0μr = μ0(1 + K)

∴ μ_r = (1 + K) .... (4)

From equation (3) and (4)

Bnet = μ0μ_rH

Calculation:

Given Magnetic Circuit,

N = 100
I = 5 A
L = 2πr = 2π × 5 × 10^-2 m

From above concept,

$H=\frac{NI}{L}=\frac{100\times 5}{10\pi \times {10}^{-2}}=\frac{5000}{\pi }$

We know that,

Bnet = μ0μrH

And, μ_r = 1000

$B_{net}=4\pi \times {10}^{-7}\times 1000\times \frac{5000}{\pi }=2T$

Concept:

The magnetic field intensity (H) of a circular coil is given by

$H=\frac{I}{2R}$

Where I is the current flow through the coil

R is the radius of the circular coil

Calculation:

Given that, Current (I) = 2 A                                             

Diameter = 1 m

Radius (R) = 0.5 m

Magnetic field intensity $H=\frac{2}{2\times 0.5}=2A/m$

Common Mistake:

The magnetic field intensity (H) of a circular coil is given by $H=\frac{I}{2R}$

The force between two current-carrying parallel conductors:

• Two current-carrying conductors attract each other when the current is in the same direction and repel each other when the currents are in the opposite direction
• Force per unit length on conductor

$\frac{F}{l}=\frac{{\mu }_0}{2\pi }\frac{i_1{i}_2}{d}$

Dynamically induced EMF: When the conductor is rotating and the field is stationary, then the emf induced in the conductor is called dynamically induced EMF.

Ex: DC Generator, AC generator

Static induced EMF: When the conductor is stationary and the field is changing (varying) then the emf induced in the conductor is called static induced EMF.

Faraday’s first law of electromagnetic induction states that whenever a conductor is placed in a varying magnetic field, emf is induced which is called induced emf. If the conductor circuit is closed, the current will also circulate through the circuit and this current is called induced current.

Faraday's second law of electromagnetic induction states that the magnitude of emf induced in the coil is equal to the rate of change of flux that linkages with the coil. The flux linkage of the coil is the product of number of turns in the coil and flux associated with the coil.

• The electric field inside a conducting sphere is zero, so the potential remains constant at the value it reaches the surface.
• When a conductor is at equilibrium, the electric field inside it is constrained to be zero.
• Since the electric field is equal to the rate of change of potential, this implies that the voltage inside a conductor at equilibrium is constrained to be constant at the value it reaches the surface of the conductor.
• A good example is the charged conducting sphere, but the principle applies to all conductors at equilibrium.