Physics-
General
Easy

Question

PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity V as shown. The force needed to maintain constant speed of EF is.

  1. fraction numerator 1 over denominator V K end fraction open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction l n open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets to the power of 2 end exponent    
  2. open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction l n open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets fraction numerator 1 over denominator K end fraction    
  3. open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction l n open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets to the power of 2 end exponent fraction numerator V over denominator R end fraction    
  4. open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction l n open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets    

The correct answer is: fraction numerator 1 over denominator V K end fraction open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction l n open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets to the power of 2 end exponent


    text Induced emf  end text stretchy integral subscript a end subscript superscript b end superscript   B v d x equals stretchy integral subscript a end subscript superscript b end superscript   fraction numerator mu subscript 0 end subscript I over denominator 2 pi x end fraction v d x
    table row cell rightwards double arrow text end text text I end text text n end text text d end text text u end text text c end text text e end text text d end text text end text text e end text text m end text text f end text text end text equals fraction numerator mu subscript 0 end subscript I v over denominator 2 pi end fraction l n invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses end cell row cell rightwards double arrow text end text text P end text text o end text text w end text text e end text text r end text text end text text d end text text i end text text s end text text s end text text i end text text p end text text a end text text t end text text e end text text d end text text end text equals fraction numerator E to the power of 2 end exponent over denominator R end fraction end cell row cell text end text text A end text text l end text text s end text text o end text text , end text text end text text p end text text o end text text w end text text e end text text r end text text end text minus F. V rightwards double arrow F minus fraction numerator E to the power of 2 end exponent over denominator V R end fraction end cell row cell rightwards double arrow F equals fraction numerator 1 over denominator V R end fraction open square brackets fraction numerator mu subscript 0 end subscript I V over denominator 2 pi end fraction C n invisible function application open parentheses fraction numerator b over denominator a end fraction close parentheses close square brackets to the power of 2 end exponent end cell end table

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