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A parallel plate capacitor of plate area A plate separation d is charged to potential difference V and then the battery is disconnected. A slab of dielectric constant K is then inserted between the plates of the capacitor so as to fill the space between the plates.If Q, E and W denotes respectively, the magnitude of charge on each plate, the electric field between the plates (after the slab is inserted), and work done on the system in the process of inserting the slab, then

  1. Q equals fraction numerator epsilon subscript 0 end subscript A F over denominator d end fraction    
  2. Q equals fraction numerator epsilon subscript 0 end subscript K A V over denominator d end fraction    
  3. E equals fraction numerator V over denominator K d end fraction    
  4. W equals fraction numerator epsilon subscript 0 end subscript A V to the power of 2 end exponent over denominator 2 d end fraction open square brackets 1 minus fraction numerator 1 over denominator K end fraction close square brackets    

The correct answer is: Q equals fraction numerator epsilon subscript 0 end subscript A F over denominator d end fraction

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Superposition of waves results in maximum and minimum of intensities such as in case of standing waves. This phenomenon is called as interference. Another type of superposition result in interference in time which is called as beats. In this case waves are analyzed at a fixed point as a function of time. If the two waves are of nearby same frequency are superimposed, at a particular point, intensity of combined waves gives a periodic peak and fall. This phenomenon is beats. If w1 and w2 are the frequencies of two waves then by superimposed y = y1 + y2 , we get at x = 0, y equals open square brackets 2 A c o s invisible function application open parentheses fraction numerator omega subscript 1 end subscript minus omega subscript 2 end subscript over denominator 2 end fraction close parentheses times t close square brackets s i n invisible function application open square brackets fraction numerator omega subscript 1 end subscript plus omega subscript 2 end subscript over denominator 2 end fraction close square brackets times t Thus amplitude frequency is small and fluctuates slowly. A beat i.e., a maximum of intensity occurs, also intensity depends on square of amplitude. The beat frequency is given by omega subscript text beat  end text end subscript equals open vertical bar omega subscript 1 end subscript minus omega subscript 2 end subscript close vertical bar Number of beats per second is called as beat frequency. A normal ear can detect only upto 10 Hz of frequency because of persistence of ear The frequency of beats produced in air when two sources of sound are activated, one emitting wavelength 32 cm, other 32.2 cm is open parentheses text  Take  end text V subscript text soud  end text end subscript equals 350 m divided by s close parentheses

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