Q27 of 31 Page 1

(a) Define mutual inductance and write its S.I. units.

(b) Derive an expression for the mutual inductance of two long co-axial solenoids of same length wound one over the other.


(c) In an experiment, two coils and are placed close to each other. Find out the expression for the emf induced in the coil c1 due to a change in the current through the coil.


a) Mutual inductance is the property of two coils by the virtue of which each opposes any change in the value of current flowing through the other by developing an induced emf. The SI unit of mutual inductance is henry and


its symbol is H.
(b) Consider two long solenoids S1 and S2 of same length l such that solenoid S2 surrounds solenoid S1 completely.


Let:


=number of turns per unit length of


=number of turns per unit length of


= Current passed through solenoid




Capture.PNG


Where,


When current is passed through solenoid, an emf is induced in solenoid .


Magnetic field linked with each turn of solenoid on passing current through it is given by:



Magnetic flux linked with each turn of solenoid will be equal to times the area of cross-section of solenoid .


Magnetic flux linked with each turn of solenoid . Therefore, total magnetic flux linked with the solenoid is given by:





Where, is the total number of turns wound over the secondary coil.



Similarly the mutual inductance between the two solenoids when current is passed through solenoid and induced emf is produced in solenoid is is given by:



Where, N1is the total number of wounds over primary coil.


More from this chapter

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25

A group of students while coming from the school noticed a box marked “Danger H.T. 2200 V” at a substation in the main street. They did not understand the utility of such a high voltage, while they argued, the supply was only 220 V. They asked their teacher this question the next day. The teacher thought it to be an important question and therefore explained to the whole class.

Answer the following questions:


(i) What device is used to bring the high voltage down to low voltage of A.C. current and what is the principle of its working?


(ii) Is it possible to use this device for bringing down the high dc voltage to the low voltage? Explain.


(iii) Write the values displayed by the students and the teacher.


 26

(a) State Ampere’s circuital law. Use this law to obtain the expression for the magnetic field inside an air cored toroid of average radius ‘r’, having ‘n’ turns per unit length and carrying a steady current I.

(b) An observer to the left of a solenoid of N turns each of cross section area ‘A’ observes that a steady current I in it flows in the clockwise direction. Depict the magnetic field lines due to the solenoid specifying its polarity and show that it acts as a bar magnet of magnetic moment m = NIA.


 28

(a) Using Huygens’s construction of secondary wavelets explain how a diffraction pattern is obtained on a screen due to a narrow slit on which a monochromatic beam of light is incident normally.

(b) Show that the angular width of the first diffraction fringe is half that of the central fringe.


(c) Explain why the maxima at become weaker and weaker with


increasing n.


 29

(a) A point object ‘O’ is kept in a medium of refractive index n1 in front of a convex spherical surface of radius of curvature R which separates the second medium of refractive index n2 from the first one, as shown in the figure. Draw the ray diagram showing the image formation and deduce the relationship between the object distance and the image distance in terms of , and R.

(b) When the image formed above acts as a virtual object for a concave spherical surface separating the medium from ( > ), draw this ray diagram and write the similar (similar to (a)) relation. Hence obtain the expression for the lens maker’s formula.