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Test: Electromagnetic Theory - 2

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Test: Electromagnetic Theory - 2 - Question 1

Example of spherical system in the following is

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 1

From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this case will be a spherical system. Thus it is charged in space.

Test: Electromagnetic Theory - 2 - Question 2

Consider sphere of radius R having uniform volume charge density ρ is rotating about it diameter. The magnetic dipolemoment of this charge distribution is

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 2

Test: Electromagnetic Theory - 2 - Question 3

A spherical conductor of radius r1 has surface charge density σ. There is an another sphere of radius r2 (r2 > r1) and this sphere is grounded by connecting with the battery of 5 volt. The potential difference between the points lies on the surface of sphere having radius r1 and outer surface of the sphere of radius r2 is

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 3

According to Gauss law, wre can write tlie electnc field

Test: Electromagnetic Theory - 2 - Question 4

Electric field in a configuration is given by  where A and k are constants, the charge density corresponding to the electric field is given by

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 4

Test: Electromagnetic Theory - 2 - Question 5

A sphere of radius r having uniform volume charge density ρ consists. Three cavities of radius r1, r2, r3 inside. If the centres of these cavities are located at the distances  respectively from die centre of the sphere the sum of electromagnetic field in the cavities will be

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 5

Suppose a sphere carrying uniform charge density ρ. Now if we make any cavity inside the sphere then the electric field inside the cavity is uniform and is given by

Test: Electromagnetic Theory - 2 - Question 6

Two homogeneous cylindrical dielectncal regions, region-1 (s < 4 cm) and region-2 (s > 4 cm) have dielectric constants 3.5 and 1.5, respectively. If  then the value of  is given by

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 6

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 7

The charge density ρ(c/m)3 is uniformly distributed in the volume of the cylinder between and then the flux density  for r > 5 a will be ______

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 7

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 8

A electromagnetic wave  is passing through a medium of refractive index 1.5. If the phase velocity is 2 * 108 m/s then the angular frequency of the wave will be 10n radian/sec. The value of n will be_________

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 8

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Test: Electromagnetic Theory - 2 - Question 9

Consider a electromagnetic wave propagating in free space. If  A /m , then the absolute value of E / H is_________________________ π( V / A ). (Answer should be an integer)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 9

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Test: Electromagnetic Theory - 2 - Question 10

A charge particle of mass M is placed below the grounded infinite conducting plate lies in xy-plane. If the distance between the charge particle and plate is 2m then the magnitude of charge particle so that it remains stationary is  The value of n is _________________ (answer should be integer)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 10

Let the magnitude of charge particle is q.
The cliarge particle will remain stationary if

Test: Electromagnetic Theory - 2 - Question 11

A plane electromagnetic wave has magnetic field  The average pointing vector is

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 11

Given  comparing this equation with standard wave equation

Test: Electromagnetic Theory - 2 - Question 12

Which one is the correct representation for vector potential  if a uniform magnetic field of magnitude B0 is applied along x-direction.

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 12

We know that curl of A
if we choose option (c)

Test: Electromagnetic Theory - 2 - Question 13

A magnetic dipole of moment  is placed in a magnetic field,  The force on the dipole is given by

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 13

The magnetostatics energy of the magnetic dipole when we placed it in the external magnetic field is

Therefore, force on the dipole is

Test: Electromagnetic Theory - 2 - Question 14

Suppose a current-carrying wire has bent in the shape ass shown in the figure. The triangular part is an equilateral triangle of side a and the linear parts are assumed to be very long. The magnetic field at the centroid of the triangle is

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 14

The given figure have two parts. So, total magnetic field at the centroid is due to linear part plus triangular part. The magnetic field at O is given by

Test: Electromagnetic Theory - 2 - Question 15

A left circularly polarized beam  is incident on a crystal (with its optical axis cut parallel to the surface) if  then the state of polarization of the emergent beam will be

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 15

Electric field for the incident beam
(∴ for left polarization phase of y-axis is greater)

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 16

A parallel-plate capacitor is charged to a potential V0, charged Q0 and then disconnected from the battery. The separation of the plates is then halved. The change of electrostatic energy is ____________Q0V0.
(Round off to two decimal places)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 16

Initial charge on the plates and potential difference between the plates are Q0 and V0 respectively. So, the electrostatic energy is stored inside the capacitor is

Now, if we reduce tlie separation between two plates by a factor 1/2 keeping charge fixed, tlie potential difference two plates wil be
Tlierefore, the final electrostatic energy is stored inside the capacitor is,

Therefore, the charge of electrostatic energy;

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 17

Suppose a current density in a long cylindrical conductor kept along r-direction is  where k is constant and r is radial distance from the axis of cylinder the magnetic induction  inside the conductor at distance a /2 from the axis of cylinder is ______  (Upto second decimal place)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 17

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Test: Electromagnetic Theory - 2 - Question 18

Aii unpolarized light is passed through the arrangement of quarter-wave plate and polarizers as shown in figure. The intensity of light after passing through P4 will be ______ I0.

Dotted lilies shows the pass axis of polarizer and in polarizer 'P3' z-axis is the pass axis.

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 18

Q.W.P. will not affect unpolarized light

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 19

A light of intensity I incident on a perfect reflecting wall of angle 30° with the normal to the wall. The pressure
on the wall will be ______ I/C. (answer should be upto one decimal places)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 19

Consider n number of photon incident on the wall per second.
Therefore, the change of momentum per second

Therefore, force applied by the photon on the wall is

*Answer can only contain numeric values
Test: Electromagnetic Theory - 2 - Question 20

A sphere of linear dielectric material lias embedded in it a uniform free charge density ρ. If its radius R and its dielectric constant (k = 2), the potential at the centre of the sphere is ______  (Round off to two decimal places)

Detailed Solution for Test: Electromagnetic Theory - 2 - Question 20

According to Gauss' law

Corresponding electric field is equal to

Therefore, the electric static potential at the centre of the sphere is

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