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NEET AIPMT SOLVED PAPER SCREENING 2005

  • question_answer
                    An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B, at the centre of the circle. The radius of the circle is proportional to:                                                                        

    A)                 \[\frac{B}{v}\]                  

    B)                 \[\frac{v}{B}\]                  

    C)                 \[\sqrt{\frac{v}{B}}\]     

    D)                 \[\sqrt{\frac{B}{v}}\]

    Correct Answer: C

    Solution :

                              The time period of electron moving in a circular orbit                 \[T=\frac{circumference\,of\,circular\,path}{speed}\]                 \[=\frac{2\pi r}{v}\]                 and equivalent current due to electron flow                 \[I=\frac{e}{T}=\frac{e}{(2\pi r/v)}=\frac{ev}{2\pi r}\]                 Magnetic field at centre of circle                 \[B=\frac{{{\mu }_{0}}I}{2r}=\frac{{{\mu }_{0}}ev}{4\pi {{r}^{2}}}\]                         \[\Rightarrow r\,\propto \,\,\sqrt{\frac{v}{B}}\]


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