Q26 of 26 Page 1

(a) Describe, with the help of a suitable diagram, how one can demonstrate that emf can be induced in a coil due to the change of magnetic flux. Hence state Faraday’s law of electromagnetic induction.

(b) Two loops, one rectangular of dimensions 10 cm x 2 �5 cm and second of square shape of side 5 cm are moved out of a uniform magnetic field perpendicular to the planes of the loops with equal velocity as is shown in the figure.


(i)In which case will the emf induced be more?


(ii)In which case will the current flowing through the two loops be less?


Justify your answer.


OR


(a)State the principle of an a.c. generator.


(b)Explain briefly, with the help of labelled diagram, its working and obtain the expression for the emf generated in the coil.


(c)Draw a schematic diagram showing the nature of the alternating emf generated by the rotating coil in the magnetic field during one cycle.


(a) The following diagram illustrates emf being induced in a coil due to a moving magnet. Moving a magnet changes the magnetic flux through the loop. Changing flux induces magnetic field.


When the south pole of the magnet moves towards the coil, a south pole in induced by the current flowing in the loop. Similarly, when the magnet moves away from the coil, a north pole is induced in the loop.



The emf () induced in the coil is related to theS magnetic flux() as:



(b) We know that the emf () induced in the coil is related to the magnetic flux() as:



Here, magnetic flux is



Where x in the length of the wire and y is the breadth.


As the coil is moved out, the length changes according the velocity as




(i)Now, velocity of both loops is same but the breadth y of square loop is more than that of rectangular loop. Hence, the emf induced will be more in square loop.


(ii) As rectangular loop has higher resistance (more wire length) than the square loop, the current would be less in the rectangular loop.


However, as the field is constant and the loops are moving within the field region, there will be no emf induced in either loops.


OR


(a) AC generator is a device which converts mechanical energy into electrical energy in form of alternating current(AC). AC generator works on the principle of electromagnetic induction. As the coil, placed in between the two poles of the magnet, rotates, the changing area induces a current in the coil.


(b) The following diagram illustrates an AC generator.



Here, the coil is mechanically rotated at angular velocity . The angle between the area vector A and the magnetic field B changes as



Now, the magnetic flux is given by



Therefore, the induced emf for a coil of N turns is




(c) The following diagram shows the induced emf as time propagates.



More from this chapter

All 26 →
22

Define the electric resistivity of a conductor.

Plot a graph showing the variation of resistivity with temperature in the case of a (a) conductor, (b) semiconductor.


Briefly explain, how the difference in the behavior of the two can be explained in terms of number density of charge carriers and relaxation time.


 23 SECTI

Asha’s uncle was advised by his doctor to have an MRI (magnetic resonance imaging) scan of his brain. Her uncle felt that it was too expensive and wanted to postpone it. When Asha learnt about this, she took the help of her family and when she approached the doctor, he also offered a substantial discount. She thus convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The resulting information greatly helped his doctor to treat him properly.

Based on the above paragraph, answer the following questions:


(a)What according to you are the values displayed by Asha, her family and the doctor?


(b)What in your view could be the reason for MRI test to be so expensive?


(c)Assuming that MRI test was performed using a magnetic field of 0 �1 T, find the maximum and minimum values of the force that the magnetic field could exert on a proton (charge = ) that was moving with a speed of .


 24

(a) Derive the expression for the potential energy of an electric dipole of dipole moment placed in a uniform electric field .

Find out the orientation of the dipole when it is in (i) stable equilibrium, (ii) unstable equilibrium.


(b) Figure shows a configuration of the charge array of two dipoles. Obtain the expression for the dependence of potential on r for r >> a for a point P on the axis of this array of charges.


OR


(a)Define electric flux. Write its S.I. unit.


(b)Using Gauss’s law, obtain the electric flux due to a point charge ‘q’ enclosed in a cube of side ‘a’.


(c)Show that the electric field due to a uniformly charged infinite plane sheet at any point distant x from it, is independent of x.


 25

(a) Define a wavefront.

(b) Using Huygens’ principle, draw the diagrams to show the nature of the wavefronts when an incident plane wavefront gets


(i)reflected from a concave mirror,


(ii)refracted from a convex lens.


(c) Draw a diagram showing the propagation of a plane wavefront from denser to a rarer medium and verify Snell’s law of refraction.


OR


(a)A concave mirror produces a real and magnified image of an object kept in front of it. Draw a ray diagram to show the image formation and use it to derive the mirror equation.


(b)A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is


(i)a convex lens of focal length 20 cm,


(ii)a concave lens of focal length 16 cm?