Science
Ingestion-and-Digestion-1
Easy

Question

Two positrons (e+) and two protons (P) are kept on four corners of a square of side a as shown in figure. The mass of proton is much larger than the mass of positron. Let q denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be

  1. fraction numerator q to the power of 2 end exponent over denominator 4 pi ϵ subscript 0 end subscript a end fraction open parentheses 1 plus fraction numerator 1 over denominator 2 square root of 2 end fraction close parentheses comma fraction numerator q to the power of 2 end exponent over denominator 4 pi ϵ subscript o end subscript a end fraction open parentheses 1 plus fraction numerator 1 over denominator 2 square root of 2 end fraction close parentheses  
  2. fraction numerator q to the power of 2 end exponent over denominator 2 pi ϵ subscript 0 end subscript a end fraction comma fraction numerator q to the power of 2 end exponent over denominator 4 square root of 2 pi ϵ subscript 0 end subscript a end fraction  
  3. fraction numerator q to the power of 2 end exponent over denominator 4 pi ϵ subscript 0 end subscript a end fraction comma fraction numerator q to the power of 2 end exponent over denominator 4 pi ϵ subscript 0 end subscript a end fraction  
  4. fraction numerator q to the power of 2 end exponent over denominator 2 pi ϵ subscript 0 end subscript a end fraction open parentheses 1 plus fraction numerator 1 over denominator 4 square root of 2 end fraction close parentheses comma fraction numerator q to the power of 2 end exponent over denominator 8 square root of 2 pi ϵ subscript 0 end subscript a end fraction  

The correct answer is: fraction numerator q to the power of 2 end exponent over denominator 2 pi ϵ subscript 0 end subscript a end fraction comma fraction numerator q to the power of 2 end exponent over denominator 4 square root of 2 pi ϵ subscript 0 end subscript a end fraction


    As mass of proton mass of positron so initial acceleration of positron is much larger than proton. Therefore positron reach far away in very short time as compare to proton

    2 K subscript e to the power of ´ end exponent end subscript equals open parentheses fraction numerator 4 k q to the power of 2 end exponent over denominator a end fraction plus fraction numerator 2 k q to the power of 2 end exponent over denominator a square root of 2 end fraction close parentheses minus fraction numerator k q to the power of 2 end exponent over denominator a square root of 2 end fraction rightwards double arrow K subscript e to the power of ´ end exponent end subscript equals fraction numerator q to the power of 2 end exponent over denominator 2 pi ϵ subscript 0 end subscript a end fraction open parentheses 1 plus fraction numerator 1 over denominator 4 square root of 2 end fraction close parentheses text  and  end text 2 K subscript p end subscript equals fraction numerator k q to the power of 2 end exponent over denominator a square root of 2 end fraction minus 0 rightwards double arrow K subscript p end subscript equals fraction numerator q to the power of 2 end exponent over denominator 8 square root of 2 pi ϵ subscript 0 end subscript a end fraction

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