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JIPMER Jipmer Medical Solved Paper-2010

  • question_answer
    An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform magnetic field B. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

    A)  \[\frac{r}{4}\]          

    B)                         \[\frac{r}{2}\]                  

    C)         2r                          

    D)         4r

    Correct Answer: D

    Solution :

    In a perpendicular magnetic field, Magnetic force = centripetal force \[i.e,\]  \[Bqv=\frac{m{{v}^{2}}}{r}\Rightarrow r=\frac{mv}{Bq}\] \[\therefore \]  \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{{{v}_{1}}}{{{v}_{2}}}\times \frac{{{B}_{2}}}{{{B}_{1}}}\] \[\frac{{{r}_{1}}}{{{r}_{2}}}=\frac{1}{2}\times \frac{1}{2}\] \[{{r}_{2}}=4{{r}_{1}}\]                 \[\Rightarrow \]               \[{{r}_{2}}=4r\]


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