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

Correct option is : (1) Reflected light is completely polarized and the angle of reflection is close to 60°

Using Brewster's law

μ = tan θ_p

⇒ 1.73 = tan θ_p

⇒ √3 = tan θ_p

⇒ θ_p = 60°

Calculation:

Calculation of Kinetic Energy (K)

We already know the minimum velocity v₀ is 3 m/s. From equation (i), the potential at origin (x = 0) is:

V₀ = 1.8 × 10⁴ × √[8 / (27/2 + x²) − 1 / (3/2 + x²)] ≈ 2.4 × 10⁴ V

Let K be the kinetic energy of the particle at origin. Applying energy conservation at x = 0 and x = ∞:

K + q₀V₀ = 1/2 m v₀² But 1/2 m v₀² = q₀V [From Eq. (ii)]

Therefore, K = q₀(V − V₀) = (10⁻⁷) × (2.7 × 10⁴ − 2.4 × 10⁴)

K = 300 × 10⁻⁶ J

Calculation:

Given the potential V = 2.7 × 10⁴ volts, applying energy conservation at x = ∞ and x = √(5/2)m:

1/2 m v₀² = q₀ V ... (i)

v₀ = √(2q₀V/m)

Substituting the values:

v₀ = √[(2 × 10⁻⁷ × 2.7 × 10⁴) / (6 × 10⁻⁴)]

v₀ = 3 m/s. Therefore, the minimum value of v₀ is 3 m/s.

Explanation:

In a Magnetic Circuit:

Definition: A magnetic circuit is a path followed by magnetic flux. It is analogous to an electrical circuit but uses magnetic fields instead of electric currents. The primary components of a magnetic circuit include magnetic flux (Φ), magnetomotive force (MMF), and reluctance (R).

Working Principle: The magnetomotive force (MMF) in a magnetic circuit is created by a current passing through a coil of wire, creating a magnetic field. This MMF drives the magnetic flux through the magnetic circuit. The relationship between MMF, magnetic flux, and reluctance is given by:

MMF = Φ × R

where:

• MMF (magnetomotive force) is measured in Ampere-Turns (A-t).
• Φ (magnetic flux) is measured in Webers (Wb).
• R (reluctance) is measured in Ampere-Turns per Weber (A-t/Wb).

Reluctance: Reluctance is the opposition to the creation of magnetic flux in the magnetic circuit. It is analogous to resistance in an electrical circuit. The reluctance depends on the length (l) and cross-sectional area (A) of the magnetic path, as well as the material's permeability (μ), and is given by:

R = l / (μ × A)

where:

• l is the length of the magnetic path.
• μ is the permeability of the material.
• A is the cross-sectional area of the magnetic path.

Correct Option Analysis:

The correct option is:

Option 3: The magnetic flux will decrease.

Explanation: According to the relationship MMF = Φ × R, if the reluctance (R) increases and the magnetomotive force (MMF) remains constant, the magnetic flux (Φ) must decrease. This is because the reluctance provides greater opposition to the magnetic flux, thereby reducing its magnitude. An increase in reluctance means that it is harder for the magnetic flux to pass through the magnetic circuit, resulting in a decrease in the magnetic flux.

Important Information

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

Option 1: The magnetomotive force (MMF) will increase.

This option is incorrect because the magnetomotive force (MMF) is a function of the current and the number of turns in the coil (MMF = N × I). An increase in reluctance does not inherently increase the MMF; instead, it affects the magnetic flux (Φ) for a given MMF.

Option 2: The magnetic flux will increase.

This option is incorrect because, as explained, an increase in reluctance leads to a decrease in magnetic flux, not an increase. The opposition to the magnetic flux becomes greater, reducing the amount of flux in the circuit.

Option 4: The resistance to magnetic flux will decrease.

This option is incorrect because reluctance is the magnetic equivalent of resistance. If the reluctance increases, the opposition (or resistance) to the magnetic flux increases, not decreases.

Conclusion:

Understanding the relationship between MMF, magnetic flux, and reluctance is crucial in analyzing magnetic circuits. When the reluctance of a path in a magnetic circuit increases, the magnetic flux decreases if the MMF remains constant. This fundamental principle helps in the design and analysis of magnetic circuits in various electrical and electronic applications.

The correct answer is 2) They require line-of-sight transmission.   

Concept:

Microwaves are electromagnetic waves with frequencies ranging from roughly 300 MHz to 300 GHz. In unguided media (like air or space), they travel in straight lines.   
Line-of-sight transmission means that there must be a direct, unobstructed path between the transmitting and receiving antennas. Obstacles like buildings, hills, and even heavy rain can significantly attenuate or block microwave signals.
Let's look at why the other options are incorrect:

1. They are slower than radio waves. All electromagnetic waves, including microwaves and radio waves, travel at the speed of light in a vacuum and very close to the speed of light in the atmosphere. There is no significant speed difference between them.   
2. They are not affected by obstacles like buildings or hills. As mentioned earlier, microwaves are indeed affected by obstacles. Their relatively short wavelengths (compared to some radio waves) make them more susceptible to blockage and reflection by such objects.
3. They use fiber optics for data transmission. Fiber optics is a guided medium, where data is transmitted as light pulses through glass or plastic fibers. Microwaves, by definition in this context ("unguided media"), propagate through the air or space without a physical guide.

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.

\(\overset{\rightharpoonup}{D} = \varepsilon \overset{\rightharpoonup}{E}\)

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

\(F' = k\frac{q_1 q_2}{r'^2} = k\frac{q_1 q_2}{(2r)^2}\)

\(\implies F' = k\frac{q_1 q_2}{4r^2} = \frac{1}{4}k\frac{q_1 q_2}{(r)^2}\)     ---(2)

From (1) and (2)

\(\implies F' = \frac{F}{4}\)

or

\(\implies F' = \frac{200N}{4} = 50 \ N\)

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

\(\frac{{{B_{net}}}}{H} = \frac{{{μ _0}H\left( {1 + K} \right)}}{H} \)

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,

\(H=\frac{NI}{L}=\frac{100× 5}{10π × 10^{-2}}=\frac{5000}{π}\)

We know that,

Bnet = μ0μrH

And, μ_r = 1000

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

Concept:

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

\(H = \frac{I}{{2 R}}\)

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 \(H = \frac{2}{{2 \times 0.5}} = 2\;A/m\)

Common Mistake:

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

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.