A square metal sheet of  is placed on the  plane as shown in the figure below.

If the surface charge density (in  ) on the sheet is , then the total charge (in , rounded off to the nearest integer) on the sheet is _________.

An electric field of  is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of .

The current (in Amperes, rounded off to two decimal places) flowing through the wire is _________.

Two resistors are connected in a circuit loop of area , as shown in the figure below. The circuit loop is placed on the  plane.

When a time-varying magnetic flux, with flux-density  (in Tesla), is applied along the positive -axis, the magnitude of current  (in Amperes, rounded off to two decimal places) in the loop is _________.

Let  be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for the vector fields

A uniform plane wave with electric field  is travelling in the air (relative permittivity,  and relative permeability,  ) in the  direction ( is a positive constant,  is the unit vector along the  axis). It is incident normally on an ideal electric conductor (conductivity,  ) at . The position of the first null of the total magnetic field in the air (measured from , in metres) is

Let  and  represent density and velocity, respectively, at a point  and time t. Assume  is continuous. Let  be an arbitrary volume in space enclosed by the closed surface  and  be the outward unit normal of  Which of the following equations is/are equivalent to  ?

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is  ). The displacement current (in Amperes) through the capacitor is ________.

In an electrostatic field, the electric displacement density vector, , is given by

where  are the unit vectors along -axis, -axis, and -axis, respectively. Consider a cubical region  centered at the origin with each side of length , and vertices at  . The electric charge enclosed within  is ________ C (rounded off to two decimal places).

In the table shown, List-I and List-II respectively, contain terms appearing on the left-hand side and the right-hand side of Maxwell’s equations (in their standard form). Match the left-hand side with corresponding right-hand side

What is the electric flux through a quarter cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?

Two identical copper wires W1 and W2 placed in parallel as shown in the figure, carry current I and 2I respectively, in opposite direction. If the two wires are separated by a distance of 4r, then the magnitude of the magnetic field between the wires at a distance r from W1 is

Two conducting spheres S1 and S2 of radii a and b (b > a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure.

For some charge placed on this structure, the potential and surface electric field on S1 are  and , and that on S2 are  and , respectively. Then, which of the following is CORRECT?  

If the vector function

 is irrotational, then the values of the constants , respectively, are

An electron is moving in free space with velocity towards a stationary electron far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is ____________ .

[Given, mass of electron , charge of electron , and permittivity ]

Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of ,  and , respectively. The value of  required to ensure that the electric flux density   at radius 10 m is______________

The current density in a medium is given by

The total current and the average current density flowing through the portion of a spherical surfaceare given, respectively, by

A uniform and constant magnetic field  exists in the direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity. Given that B, m, q,  and  are all non-zero, which one of the following describes the eventual trajectory of the particle?

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is 𝐸 when the plate separation is d. The capacitor is then isolated electrically and the plates are moved such that the plate separation becomes 2d.

At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?

A positive charge q is placed at x=0 between two infinite metal plates placed at x=-d and at x=+d respectively. The metal plates lie in the yz plane.

The charge is at rest at t=0, when a voltage +V is applied to the plate at -d and voltage -V is applied to the plate at x=+d. Assume that the quantity of the charge 𝑞 is small enough that it does not perturb the field set up by the metal plates. The time that the charge q takes to reach the right plate is proportional to

Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?

Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of Hφ on r, where Hφ is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor?

In a source free region in vacuum, if the electrostatic potential, the value of constant c must be _______.

The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression

The type of the polarization is

A coaxial capacitor of inner radius 1 mm and outer radius 5 mm has a capacitance per unit length of 172pF/m. If the ratio of outer radius to inner radius is doubled, the capacitance per unit length (in pF/m) is ________.

The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity ∈ is

Given the vector

,

where  denote unit vectors along xy directions, respectively. The magnitude of curl of A is ________.

A region shown below contains a perfect conducting half-space and air. The surface current  on the surface of the perfect conductor is  amperes per meter. The tangential  field in the air just above the perfect conductor is

The electric field (assumed to be one-dimensional) between two points A and B is shown. Let  and  be the electrostatic potentials at A and B, respectively. The value of  in Volts is ________.

Given . If S represents the portion of the sphere  for z ≥ 0 , then  is______________.

If   is the electric field in a source free region, a valid expression for the electrostatic potential is  

The divergence of the vector field   is

An infinitely long uniform solid wire of radius a carries a uniform dc current of density j.

The magnetic field at a distance r from the center of the wire is proportional to

An infinitely long uniform solid wire of radius a carries a uniform dc current of density j.

A hole of radius b (b < a) is now drilled along the length of the wire at a distance d from the center of the wire as shown below.

The magnetic field inside the hole is

A current sheet  A/m lies on the dielectric interface x=0 between two dielectric media with,  in Region-1  and ,  in Region-2 . If the magnetic field in Region-1 at  is A/m, the magnetic field in Region-2 at  is

 (Region-2): ,

 (Region-1): ,

Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y-z plane and parallel to the y-axis. The other wire is in the x-y plane and parallel to the x-axis. Which components of the resulting magnetic field are non-zero at the origin?

A magnetic field in air is measured to be

What current distribution leads to this field?

[Hint: The algebra is trivial in cylindrical coordinates.]

For static electric and magnetic fields in an inhomogeneous source-free-medium, which of the following represents the correct form of two of Maxwell’s equations?

If C is a closed curve enclosing a surface S, then the magnetic field intensity, the current density and the electric flux density  are related by

A medium is divided into regions I and II about x = 0 plane, as shown in the figure below. An electromagnetic wave with electric field  is incident normally on the interface form region-I. The electric field  in region-II at the interface is:

A parallel plate air-filled capacitor has plate area of  and plate separation of . It is connected to a 0.5 V, 3.6 GHz source. The magnitude of the displacement current is

The unity of  is

Medium 1 has the electrical permittivity   farad/m and occupies the region to the left of  plane. Medium 2 has the electrical permittivity   farad/m and occupies the region to the right of plane. If  in medium 1 is volt/m, then  in medium 2 is

If the electric field intensity is given by volt/m, the potential difference between X (2,0, 0) and Y (1, 2, 3) is

If the electric field intensity associated with a uniform plane electromagnetic wave travelling in a perfect dielectric medium is give by

 volt/m, then the velocity of the travelling wave is

Distilled water at 25º C is characterized by mho/m and  at a frequency of 3 GHz. Its loss tangent tan δ is

The electric field on the surface of a perfect conductor is 2 V/m. The conductor is immersed in water with . The surface charge density on the conductor is

Given  in free space.

(a) Write all the four Maxwell’s equations in free space.

(b) Find .        (c) Find H

An electric field on a plane is described by its potential  where r is the distance from the source. The field is due to

The Maxwell equation  is based on

A loop is rotating about the y-axis in a magnetic field . The voltage in the loop is

Given an irrotational vector field

Find .  at (1, 1, -2)

A metal sphere with 1 m radius and a surface charge density of  is enclosed in a cube of 10 m side. The total outward electric displacement normal to the surface of the cube is

Match the following

The electric field strength at a distance point, P, due to a point charge, +q. located on the origin, is . If the point charge is now enclosed by a perfectly conducting metal sheet sphere whose centre is at the origin, then the electric field strength at the point. P. outside the sphere becomes.        

In the infinite plane, , there exists a uniform surface charge density of . The associated electric field strength is

Match list I and list II and select answer using the code given below:-

(a)

(b)  

(c)

(1) Continuity equation                

(2) Faraday’s law

(3) Ampere’s law                        

(4) Gauss’s law

(5) Biot-Savart law

For a uniformly charged sphere of radius R and charge density p, the ratio of magnitude of electric fields at distance  and 2R from the centre, i.e.,

 is ___________

A long solenoid of radius R, and having N turns per unit length carries a time dependent current. The magnitude of induced electric field at a distance  radially from the axis of the solenoid is

Match the following descriptions with each of the diagrams given in figure. Fields are near the interface, but on opposite sides of the boundary. Vectors are drawn to scale.

(a) Medium 1 and medium 2 are dielectrics with
(b) Medium 1 and medium 2 are dielectrics with
(c) Medium 2 is a perfect conductor

(d) Medium 1 is a perfect conductor.