Q31 of 31 Page 1

(a) Explain, using suitable diagrams, the difference in the behavior of a

(i) Conductor and (ii) dielectric in the presence of external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.


(b) A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge Q/2 is placed at its centre C and another charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.


(a) (i) CONDUCTOR


= external field


= internal field created by the redistribution of electrons inside the metal.


When a conductor like a metal is subjected to external electric field, the electrons experience a force in the opposite direction collecting on the left hand side.


A positive charge is therefore induced on the right hand side. This creates an opposite electric field () that balance out


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The net electric field inside the conductor becomes zero.


(iii) DIELECTIRC:


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When external electric field is applied, dipoles are created (in case of non-polar dielectrics). The placement of dipoles is as shown in the given figure. An internal electric field is created which reduces the external electric field.
Polarization of dielectric (P) is defined as the dipole moment per unit volume of the polarized dielectric.


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Where, = susceptibility and E= electric field.


(b) Net force on the charge, placed at the centre of the shell, is zero.


Force on change 2Q kept at a point A


F=E× 2Q=


Electric flux through the shell,


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27

(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.


 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.


 30

(a) An electric dipole of dipole moment consists of point charges +q and –q separated by a distance 2a apart. Deduce the expression for the electric field due to the dipole at a distance x from the centre of the dipole on its axial line in terms of the dipole moment. Hence show that in the limit

(b) Given the electric field in the region=, find the net electric flux through the cube and the charge enclosed by it.


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