Electromagnetic Theory MCQ Quiz in বাংলা - Objective Question with Answer for Electromagnetic Theory - বিনামূল্যে ডাউনলোড করুন [PDF]

Explanation:

Given: 

Now, at ,  (given)

• We will take potential inside the cavity only so 
• \

Now,   =>  

----------------------1(For )

• Now, according to Legendre polynomial, 
• Substitute values of  in equation 1, we get,

​

• Compare values of , to find the values of , we get,

​

 (for )

• Substitute values of in above equation, we get,

​

• Potential at a distance R/2 from the center of the sphere i.e. for 

So, the correct answer is .

Concept:

When the coil is flipped (i.e., the direction of its axis is reversed) the angle changes from 0° to  and for the value of induced emf, we will use the induced emf formula in terms of rate of change of magnetic flux.

Formula Used-

•  where magnetic flux

Explanation:

• B = magnetic field
• =Area of circular coil
• N=Number of turns in the coil

Now, take the formula of emf in terms of magnetic flux,

• ---------1

Now, (Given)

Equation 1, becomes

• , take 

Taking integration on both sides and taking the limits from 0° to , we get,

Put , we get

So, the correct answer is .

Option: (3) linearly polarized along the y-direction

Explanation:

A charged particle is moving uniformly on the xy-plane along a circle of radius centered at the origin. A charged particle executes its orbit with angular frequency (rad/s), and a detector is put at a distance d on the x-axis to detect the electromagnetic wave radiated by the particle along the x-direction. The detector detects an electric field vector  lying in the y-plane of the orbit and oscillates sinusoidally in magnitude with the orbital frequency and the magnetic field is in the z-direction. At d>>a, the wave received by the detector is linearly polarized along the y-direction.

CONCEPT:

In uniform velocity we are having zero force, the electric field is written as;

F = 0

⇒ 

and third maxwell's equation is written as;

CALCULATION:

As we have;

 -----(1)

and  -----(2)

Now, from equations 1) and 2) we have;

Hence option 1) is the correct answer.

Concept:

The relationship between the electric field E_o The relationship between the electric field B_o in an electromagnetic wave propagating through a vacuum is governed by the equation derived from Maxwell's equations.

Calculation: 

For an electromagnetic wave in a vacuum, the speed of the wave c  is related to E_o and B_o as

Also c = 

⇒ 

⇒ kE_o = ωB_o

∴ the correct relation between E0 and B0 is kEo = ωBo

The correct answer is Microwaves.Key Points

• The option with the highest wavelength among the given electromagnetic waves is microwaves.
• Microwaves have wavelengths ranging from 1 millimeter to 1 meter.
• Microwaves move in a straight line.
• Within the electromagnetic spectrum, microwaves have a frequency that is higher than that of regular radio waves and lower than that of infrared light.
• They are employed in radar, communications, radio astronomy, remote sensing, and, of course, cooking because of their heating function.

Additional Information

• Infrared waves have wavelengths ranging from 700 nanometers to 1 millimeter.
  • They are commonly used in heating and communication applications.
• Ultraviolet waves have wavelengths ranging from 10 nanometers to 400 nanometers.
  • They are commonly used in sterilization and detection applications.
• X-rays have wavelengths ranging from 0.01 nanometers to 10 nanometers.
  • They are commonly used in medical imaging and material analysis applications.

Explanation: 

• We have the total electric field E and magnetic field B as:

• Now, let's find the Poynting vector  using these total electric and magnetic fields:

• Calculating the vector cross product, 
• Here, the Poynting vector is given as along the direction î + ĵ.
• This implies that the î and ĵ components of  must be equal.
• Therefore, 
• Dividing through by EB (it's not zero),

We get: -α -1 = β

• Rearranging, we get: α + β + 1 = 0

Concept:

• The transmission coefficient (T) for an electromagnetic wave moving from a vacuum into a medium with refractive index (n) is given by: 
• This coefficient (T) is also expressed as the ratio of the amplitude of the transmitted wave (E_t) to the amplitude of the incident wave (E₀): 

Explanation:

• The refractive index of the vacuum is : 
• In the problem, it states that .
• Substituting the value in the formula of the coefficient of transmission: T

Concept:

The method of images is used to solve a variety of problem.

So, if we have a charge q at distance d then we can have a

image charge -q at a distance d on the other side of the infinite conducting sheet.

Now the force between the real and image charge is given as;

 , where the distance between them is 2d.

where k is .

Explanation:

We are given with the fact that a charge q is of mass m is placed at a distance d below a

grounded infinite conducting sheet which lies in the xy plane.

Now for this case for the charge to be stationary,

the force on the charge q should be 0.

There are two forces, one from the gravity and one due to its image charge.

So the total force on the charge q is given by;

 .

Now, .

Therefore .

Hence the correct option is option 1).