Solve your IGNOU Doubts

Question:

How do we differentiate between diamagnetic and paramagnetic materials? Show that for diamagnetic atoms placed in an external magnetic field $B$ , the change in dipole moment is opposite to the direction of $B$

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Question:

A 10 eV electron is circulating in a plane at right angles to a uniform magnetic field of $1.0\times10^{4}$ T. Calculate the orbital radius of the electron, cyclotron frequency, period of revolution, and the direction of circular motion of the electron as viewed by an observer looking along the magnetic field.

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Question:

A copper wire of diameter 2 mm and length 30 m is connected across a battery of 2V. Calculate the current density in the wire and drift velocity of the electrons. The resistivity of copper is $1.72\times 10^{-8}\,\Omega m\, and\,n=8.0\times10^{28}$ electrons $m^{-3}.$ .

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Question:

A glass of relative permittivity 5 is kept in an external electric field of magnitude $10^2\,Vm^{-1}$ . Calculate the polarisation vector, molecular/atomic polarisability and the refractive index of the glass.

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Question:

The capacitance of a parallel plate capacitor is increased by a factor of 6 when a dielectric material fills the space between its plates. What is the relative permitivity of the dielectric material? If this material is placed in between the plates of a cylindrical capacitor of outer and inner radii 12 cm and 10 cm respectively, calculate the capacitance per unit length of the cylindrical capacitor.

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Question:

Consider the figure given below. Charges $q_1,q_2$ and $q_3$ are placed at $P,Q$ and R, respectively, and $q_1=q_2=-q_3=2\mu C.$ Determine the magnitude and the direction of the electric field at point A.

Image ignouassignments-ignouacademy-com--p-doubts-35735

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Question:

A 100 m long thread carries charges uniformly distributed along its length. An electron, 10 cm away from the centre of the thread along a line perpendicular to the thread experiences an attractive force of $2.7\times 10^{-12}N.$ Calculate the total charge on the thread.

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Question:

What do you understand by electrostatic potential energy? Calculate the electrostatic potential energy for the system of charges shown below. Take

$q=5\,\mu C\,and\,a=2\,cm.$ Image ignouassignments-ignouacademy-com--p-solve-79982

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Question:

The initial basic feasible solution of a transportation problem is given below:

Image ignouassignments-ignouacademy-com--p-solve-55376

Check whether the given solution is optimal. If it is not, then find the optimal solution.

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Question:

Solve the following LP problem by using two-phase simplex method:

$Minimize\,z=x_1-2x_2-3x_3$

$subject\,to\,-2x_1+3x_2+3x_3=2$

$2x_1+3x_2+4x_3=1$ $x_1,x_2,x_3\geq 0$

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Question:

For the following pay-off matrix, transform the zero-sum game into an equivalent linear programming problem: Image ignouassignments-ignouacademy-com--p-your-85589

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Question:

A businessman has to get 5 cabinets, 12 desks and 18 shelves cleaned. He has two part-time employees, Anjali and Arnav. Anjali can clean 1 cabinet, 3 desks and 3 shelves in a day, while Arnav can clean 1 cabinet, 2 desks and 3 shelves in a day. Arnav is paid Image ignouassignments-ignouacademy-com--p-solve-22127 22 per day and Anjali is paid 25 per day. Formulate the problem of finding the number of days for which Anjali and Arnav have to be employed to get the cleaning done with minimum cost as a linear programming problem.

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Question:

Without sketching the region, check whether $P(0,0)$ is in the convex hull of the points $A(-1,-1),B(1,0)$ and $C(0,1).$ . If it is in the region, write P as convex combination of A,B and C.

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Question:

The electrostatic potential $v(x,y)$ in a rectangular region is governed by the two

dimensional Laplace equation: $\frac{\partial ^2(x,y)}{\partial x^2}+\frac{\partial ^2v(x,y)}{\partial y^2}=0$

and

$v(x,40)=110V$

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Question:

Using the principle of dominance, solve the game whose pay-off matrix is given below:

Image ignouassignments-ignouacademy-com--p-ignou-52464

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Question:

Test the following set for convexity. $S=\{(x,y):x+y\leq8{\mathrm{~or~}}2x+y\leq10,x\geq0,y\geq0\}.$

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Question:

Reduce the following PDE to a set of three ODEs by the method of separation of variables.

$\frac{\partial ^2u}{\partial r^2}+\frac{2}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{\partial ^2u}{\partial \Theta }+\frac{1}{r^2sin}\frac{\partial ^2u}{\partial \phi ^2}=0$