Test: Electromagnetic Theory - 1

Consider a capacitor consisting of two fixed semicircular plates of radius R separated by a distance d. A semicircular dielectric constant k almost fills up the space between the plates and passing throughthe centre. A constant potential difference V is maintained between the plates. If the slab is now rotated throughan angle θ. then the torque acting on the slab will be

A filter is used to obtain nearly mnochromatic radiation from white light. If the bandwidth of filter is 8 nm and the mean wavelength is 800 nm. The coherence lenath and coherence time of the filtered liciht are respectively

Consider the propagation of EM waves dilute ionised gases such as the ionosphere. If the electron density is
10²²/m³. The frequency of the wave that can passing through the gases is ____x 10¹⁰ Hz (your answer
should be an integer)

In good conductors  differ in phase by______ degree, (answer should be an integer)

A certain amount of charge Q is distributed on the circular and semicircular ring of equal radius.. If the electrostatic potential at the centre of the circle and semicircle is V₁ and V₂ respectively, then the ratio of V₁ and V₂ is ____  (answer should be an integer)

An electric field  exists in space. The total charge enclosed in a sphere of unit radius centred at the origin is_______ πε₀. (Answer should be an integers)

A thin disk of radius R carrying uniform surface charge density σ is rotating with constant angular velocity ω about its axis (z). Suppose there is a magnetic field  The magnitude of the torque acting on the disk is ______ πσωBR⁴ (Upto second decimal places)

A conducting loop in the shape of a right angle isosceles triangle of height 10 cm is kept such that the 90° vertex is very close to an infinitely long conducting wire. The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at a constant rate of 10 As^-1. Which of the following statement is true?

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to one of the loop and is in the plane of the loop. If steady current I is established in the wire as shown in the figure, the loop will 

Suppose a wire of radius a. length l and resistance R is carrying a steady current I with a potential difference V across the length. The poynting vector on the surface of the wire is

The electric field associated with an electromagnetic wave in certain medium is given by  The medium must be a 

Consider a waveguide of square cross-section having side a. It is to transmit an EM wave of wavelength λ. in TE₁₀ mode but not in the TE₁₁ or TM₁₁ modes. The range of values of a is

Suppose a particle of charge q and mass m enters with a velocity  a region and crossed  fields, where  If the initial velocity of the particle is  then particle will follow

Consider a simple magnetic field, which increases exponentially with time  where B₀ and α are constant. The electric field that will be produced due to the given time varing magnetic field is

The E-field associated with an electromagnetic wave in from space is described by 
The wave is incident normally on the surface (z = 0) of a perfect conductor and gets reflected. The E-field of the reflected wave tor z < 0 is

A plane polarized electromagnetic wave in free space is incident normally on the surface of a conductor having complex refractive index n = 1 + in_i. The phase shift of the electric vector of the reflected wave with respect to that of the incident wave is given by  the value of m is _______(answer should be integers)

Consider a waveguide of square cross-section having side a. It is to transmit an EM wave of wavelength λ. in TE₁₀ mode but not in the TE₁₁ or TM₁₁ modes. The range of values of a is  The value of n is ___________(answer should be an integer)