Physics-
General
Easy

Question

Work required to set up the four charge configuration (as shown in the figure) is

  1. negative 0.21 q to the power of 2 end exponent divided by epsilon subscript 0 end subscript a    
  2. negative 1.29 q to the power of 2 end exponent divided by epsilon subscript 0 end subscript a    
  3. negative 1.41 q to the power of 2 end exponent divided by epsilon subscript 0 end subscript a    
  4. plus 2.82 q to the power of 2 end exponent divided by epsilon subscript 0 end subscript a    

The correct answer is: negative 0.21 q to the power of 2 end exponent divided by epsilon subscript 0 end subscript a


    Work is required to set up the four charge configuration
    q subscript 1 end subscript equals plus q comma blank q subscript 2 end subscript equals negative q comma blank q subscript 3 end subscript equals plus q a n d q subscript 4 end subscript equals negative q

    W equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction open square brackets fraction numerator open parentheses plus q close parentheses open parentheses negative q close parentheses over denominator A B end fraction plus fraction numerator open parentheses negative q close parentheses open parentheses plus q close parentheses over denominator B C end fraction plus fraction numerator open parentheses plus q close parentheses open parentheses negative q close parentheses over denominator C D end fraction plus fraction numerator open parentheses negative q close parentheses open parentheses plus q close parentheses over denominator D A end fraction plus fraction numerator open parentheses plus q close parentheses open parentheses plus q close parentheses over denominator A C end fraction plus fraction numerator open parentheses negative q close parentheses open parentheses negative q close parentheses over denominator B D end fraction close square brackets
    W equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction open square brackets negative fraction numerator q to the power of 2 end exponent over denominator a end fraction minus fraction numerator q to the power of 2 end exponent over denominator a end fraction minus fraction numerator q to the power of 2 end exponent over denominator a end fraction minus fraction numerator q to the power of 2 end exponent over denominator a end fraction plus fraction numerator q to the power of 2 end exponent over denominator a square root of 2 end fraction plus fraction numerator q to the power of 2 end exponent over denominator a square root of 2 end fraction close square brackets
    W equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction fraction numerator q to the power of 2 end exponent over denominator a end fraction open square brackets negative 4 plus square root of 2 close square brackets equals fraction numerator 1 over denominator 4 pi epsilon subscript 0 end subscript end fraction fraction numerator q to the power of 2 end exponent over denominator a end fraction open square brackets negative 4 plus 1.414 close square brackets
    W equals negative 0.21 cross times fraction numerator q to the power of 2 end exponent over denominator epsilon subscript 0 end subscript a end fraction open parentheses a p p r o x. close parentheses

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