Q25 of 805 Page 1

(a)Write the expression for the equivalent magnetic moment of a planer current loop of area A, having N turns and carrying a current i. Use the expression to find the magnetic dipole moment of a revolving electron.

(b)A circular loop of radius r, having N turns and carrying current I, is kept in the XY plane. It is then subjected to a uniform magnetic field . Obtain expression for the magnetic potential energy of the coil-magnetic field system.


OR


(a) A long solenoid with air core has n turns per unit length and carries a current I. Using Ampere’s circuital law, derive an expression for the magnetic field B at an interior point on its axis. Write an expression for magnetic intensity H in the interior of the solenoid.


(b) A (small) bar of material, having magnetic susceptibility χ, is now put along the axis and near the centre, of the solenoid which is carrying a d.c. current through its coils. After some time, the bar is taken out and suspended freely with an unspun thread. Will the bar orient itself in magnetic meridian if (i) χ < 0 (ii) χ ˃ 1000?


Justify your answer in each case.

a) The required expression is,


M = n I A,


Where m is the magnetic dipole moment, n is the no. of turns, I is the current and A is the cross-section area of the loop.


the magnetic dipole moment of a revolving electron is found as,



The electron of charge (–e) (e = + 1.6 × 10-19 C) performs uniform circular motion around a stationary heavy nucleus of charge +Ze. This constitutes a current I, where



and T is the time period of revolution. Let r be the orbitalradius of the electron, and v the orbital speed. Then,



Which gives,



So the magnetic dipole moment can be written as,



We can also write,



Where me is the mass of the electron and l is angular momentums so,



b) The magnetic dipole moment of the loop is given as,



(± is used the direction of current is not given whether it is clockwise or anti-clockwise)


So, the magnetic potential energy is given as,



Substituting the values,



E=±Nπr2 IBz


Conclusion: -


The magnetic potential energy of the system is E = Nr2IBz


OR


a) A long wire wound in a close-packed helical structure carrying a current ‘I’ is called a solenoid. For practical applications, the length of the solenoid is taken much greater than its diameter. The magnetic field in the interior space of the solenoid can be found as the vector summation of all vector fields produced by the different individual turns which constitute the overall structure of the solenoid.



Magnetic field B is nearly uniform and parallel to the axis of the solenoid at interior points near its center and external field near the center is very small.


To find the net magnetic field intensity, assume a rectangular Amperian loop abcd. Along cd the field is zero. Alongside crosswise sections bc and ad, the field component is zero. Thus, these two sections make no contribution. Let the field along ab be B. Thus, the appropriate length of the Amperian loop is, L = h.


Let n be the number of turns per unit length, then the total number of turns is nh.


The enclosed current is, Ie = I (n h), where I is the current in the solenoid. From Ampere’s circuital law,


BL = μ0Ie,


B h = μ0(Inh) ,


B = μ0 n I


The direction of the field is given by the right-hand rule.


The magnetic intensity H, inside a solenoid with air inside is given as,



Where, is the magnetization of the material and for air is zero, so,




H=nI


b) i)for <0, the material is diamagnetic.


The materials which are diamagnetic in nature show weak, negative sensitivity towards magnetic fields. These materials are weakly repelled by magnetic fields and does not preserve the magnetic properties when the external field is removed. The bar will not orient itself in magnetic meridian.


ii)for >1000, the material is ferromagnetic.


The materials which are ferromagnetic in nature show huge, positive sensitivity towards magnetic fields. These materials are strongly attracted by magnetic fields and preserve the magnetic properties when the external field is removed. Yes the bar will orient itself in magnetic meridian.


More from this chapter

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23

Binding energy per nucleon versus mass number curve is as shown. and are four nuclei indicated on the curve


Based on the graph:


(a) Arrange X, W and S in the increasing order of stability.


(b) Write the relation between the relevant A and Z values for the following nuclear reaction.


S → X + W


(c) Explain why binding energy for heavy nuclei is low.


OR


How are protons, which are positively charged, held together inside a nucleus? Explain the variation of potential energy of a pair of nucleons as a function of their separation. State the significance of negative potential energy in this region?

 24

A sinusoidal carrier wave of amplitude AC and angular frequency ωC is modulated in accordance with a sinusoidal information signal of amplitude Am and angular frequency ωm. Show that the amplitude modulated signal contains three frequencies centered around ωC. Draw the frequency spectrum of the resulting modulated signal.

 26

(a) There are two sets of apparatus of Young’s double slit experiment. In set A, the phase difference between the two waves emanating from the slits does not change with time, whereas in set B, the phase difference between the two waves from the slits changes rapidly with time. What difference will be observed in the pattern obtained on the screen in the two set ups?

(b) Deduce the expression for the resultant intensity in both the above-mentioned set ups (A and B), assuming that the waves emanating from the two slits have the same amplitude A and same wavelength λ.


OR


(a)The two polaroids, in a given set up, are kept ‘crossed’ with respect to each other. A third polaroid, now put in between these two polaroids, can be rotated. Find an expression for the dependence of the intensity of light I, transmitted by the system, on the angle between the pass axis of first and the third polaroid. Draw a graph showing the dependence of I on ϴ.


(b)When an unpolarized light is incident on a plane glass surface, find the expression for the angle of incidence so that the reflected and refracted light rays are perpendicular to each other. What is the state of polarization, of reflected and refracted light, under this condition?

 27

a) Draw the circuit diagram to determine the characteristics of a p- n-p transistor in common emitter configuration.

b) Explain, using I-V characteristics, how the collector current changes with the base current. How can (i) output resistance and (ii) current amplification factor be determined from the I-V characteristics?


OR


a) Why are photodiodes preferably operated under reverse bias when the current in the forward bias is known to be more than that in reverse bias?


b) The two optoelectronic devices: - Photodiode and solar cell, have the same working principle but differ in terms of their process of operation. Explain the difference between the two devices in terms of (i) biasing, (ii) junction area and (iii) I-V characteristics.