Solve your IGNOU Doubts

Question:

Obtain the Fourier sine and cosine transforms for the following function:

Image ignouassignments-ignouacademy-com--p-doubts-65750

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Question:

Evaluate the integral $\int_{0}^{2\pi } \frac{d\theta }{2 + cos\theta } = \frac{2\pi }{\sqrt{3}}$ over the circle Z  4

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Question:

Obtain the analytic function whose real part is

$U ( x,y) = e^{x} cos y$

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Question:

Show that set { L, W, $W^{2}$ } forms a cyclic group of order 3 under multiplication, where w is the imaginary cube root of unity

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Question:

Define symmetric anti-symmetric tensors. Write down transformation law obeyed by the components of a

i) Contravarient tensor of rank 3, and

ii) Covariant tensor of rank 3.

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Question:

Verify the Caley-Hamilton theorem for the following matrix:

$C = \begin{bmatrix} 1 &2 &3 \\ 2&-1 &4 \\ 3 &1 &1 \end{bmatrix}$

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Question:

Show that the eigenvectors belonging to distinct eignenvlaues of a hermitian matrix are orthogonal to each other

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Question:

Determine the eigenvalues of the matrix A given below

$A = \begin{bmatrix} 0 & 2i & 3i\\ -2i &0 &6i \\ -3i&-6i & 0 \end{bmatrix}$

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Question:

Show that the matrix $B = \begin{pmatrix} 0&-i \\ i & 0 \end{pmatrix}$ is both hermitian and unitary.

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Question:

A uniform plane electromagnetic wave of 100 MHz travelling in free space strikes a large block of a material having $\varepsilon = 4 \varepsilon _{0} ,\mu = 9 \mu _{0}$ and $\ \sigma = 0$ normal to the surface. The incident electric field vector is given by

E = 500 cos $( \omega t - \beta y) z V m^{-1}$

Write the complete expressions for the reflected and transmitted electric field vectors, and the incident, reflected and transmitted magnetic field vectors.

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Question:

Using Maxwell’s equations in free space, derive the wave equation for the y-component of the electric field vector.

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Question:

Using Maxwell’s equations in free space, derive the wave equation for the y-component of the electric field vector.

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Question:

Show that in the presence of external magnetic field, the magnetisation of a paramagnetic material depends on the strength of the magnetic field and the temperature of the material

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Question:

Using Biot-Savart’s law, obtain an expression for the magnetic field due to electric current flowing in a long straight wire at a distance R from the wire along a line perpendicular to the wire.

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Question:

The number density of electrons in the aluminium metal is 9.64 $\times 10^{28} m^{-3}$ Calculate the drift velocity of electrons in an aluminium wire of cross-sectional area 4.0 mm2 in which a current of 2 A is flowing

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Question:

What is a linear conductor? Discuss the conditions under which a metal does not behave as a linear conductor.

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Question:

Three capacitors are connected to each other as shown below:

Image ignouassignments-ignouacademy-com--p-ignou-17905

Calculate the equivalent capacitance between points A and B.

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Question:

Explain how Gauss’s law is modified for dielectric material and establish the relation:

Image ignouassignments-ignouacademy-com--p-doubts-31583

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Question:

Discuss the behaviour of a dielectric in an electric field and thereby define molecular polarisability and polarisation

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Question:

Three charges 2q, 4q and 2q are to be placed on a 1.0 m long straight wire. Determine the positions where the charges should to be placed so that the potential energy of the system is a minimum.

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