Q24 of 26 Page 1

(a) Distinguish, with a help of a suitable diagram, the difference in the behavior of a conductor and a dielectric placed in an external electric field. How does polarized dielectric modify the original external field?

(b) A capacitor of capacitance C is charged fully by connecting it to a battery of emf, E. it is then disconnected from the battery. If the separation between the plates of the capacitor is now doubled, how will the following change?


(i) charge stored by the capacitor.


(ii) field strength between the plates.


(iii) Energy stored by the capacitor.


Justify your answer in each case.


OR


(a) Explain why, for any charge configuration, the equipotential surface through a point is normal to the electric field at that point.


Draw a sketch of equipotential surfaces due to a single charge (-q), depicting the electric field lines due to the charge.


(b) Obtain an expression for the work done to dissociate the system of three charges placed at the vertices of an equilateral triangle of side ‘a’ as shown below.



(a) When a conductor is placed in an external field, free charge carriers move and themselves such that induced electric field opposes the external field so that the net electrostatic field is zero.



In a dielectric, free movement is not possible. The dipole is induced by stretching or re-orienting the molecules such that the net effect of dipoles opposes the external field. This causes polarization. Thus the polarized dielectric is equivalent to two charged surfaces with induced surface charge densities.



(b) For the capacitor:


(i) The charge stored does not change because of the law of conservation of charges.


(ii) The field strength between the plates is



As field strength is independent of the distance between the plates. Field strength remains same.


(iii) The energy stored in the capacitor is



When distance between the plates is doubled, capacitance becomes half. Hence, energy stored will also double.


OR


(a) For any charge configuration, the equipotential surface through a point is normal to the electric field at that point. If field is not normal, it would have a component along the surface. To move a unit test charge against this component, work would have to be done.


This is contradiction to the definition of equipotential surface that there is no potential difference between any two points on the surface and no work is required to move a test charge on the surface. So, the equipotential surface through a point is normal to the electric field at that point.


Equipotential surface for a negative charge:



(b) Work done to keep the system bound is





So, work done to dissociate the system is



More from this chapter

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22

(i) A screen is placed at a distance of 100 cm from an object. The image of the object is formed on the screen by a convex lens for two different locations of the lens separated by 20cm. calculate the focal length of the lens used.

(ii) A converging lens is kept coaxially in contact with a diverging lens- both the lenses being of equal focal length. What is the focal length of the combination?


 23

Seema’s uncle was advised by his doctor to have an MRI (Magnetic Resonance Imaging) scan of his brain. Her uncle felt it to be expensive and wanted to postpone it.

When Seema learnt about this, she took the help of her family and also approached the doctor, who also offered a substantial discount. She then convinced her uncle to undergo the test to enable the doctor to know the condition of his brain. The information thus obtained greatly helped the doctor to treat him properly.


Based on the above paragraph, answer the following question:


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


(b) What could be the possible reason for MRI test to be so expensive?


(c) Assuming that MRI test was performed using a magnetic field of 0.1T, find the minimum and maximum values of the force that the magnetic field could exert on a proton (charge= 1.6× 10-19C) moving with a speed of 104m/s.


 25

(a) When a bar magnet is pushed towards (or away) from the coil connected to a galvanometer, the pointer in the galvanometer deflects. Identify the phenomenon causing this deflection and write the factors on which the amount and direction of the deflection depends. State the laws describing this phenomenon.

(b) Sketch the change in flux, emf and force when a conducting rod PQ of resistance R and length l moves freely to and fro between A and C with speed v on a rectangular conductor placed in uniform magnetic field as shown in figure.



OR


In a series LCR circuit connected to an a.c. source of voltage v= vmsinωt, use phasor diagram to derive an expression for the current in the circuit. Hence obtain the expression for the power dissipated in the circuit. Show that power dissipated at resonance is maximum.


 26

(a) Why does unpolarized light from a source show a variation in intensity when viewed through a Polaroid which is rotated? Show with the help of a diagram, how unpolarized light from sun gets linearly polarized by scattering.

(b) Three identical polarized sheets P1, P2 and P3 are oriented so that the pass axis of P2 and P3 are inclined at angles of 60°and 90° respectively with the pass axis of P1. A monochromatic source S of unpolarized light of intensity I˳ is kept in front of the polaroid sheet P1 as shown in figure. Determine the intensities of light as observed by the observer at O, when Polaroid P3 is rotated with respect to P2 at angles θ = 30° and 60°.



OR


(a) Derive an expression for path difference in Young’s double slit experiment and obtain the conditions for constructive and destructive interference at a point on the screen


(b) The intensity at the central maxima in Young’s double slit experiment is I˳. find out the intensity at a point where the path difference is