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AMU Medical AMU Solved Paper-2000

  • question_answer
    Electron moves at right angle to a magnetic field of \[\text{1}.\text{5}\times \text{1}{{0}^{-\text{2}}}\] T with speed of \[\text{6}\times \text{1}{{0}^{\text{7}}}\text{ m}/\text{s}.\] If the specific charge of the electron is \[\text{1}.\text{7}\times \text{1}0\text{11 C}/\text{kg}.\] The radius of circular path will be

    A)  3.31 cm                               

    B)  4.31 cm

    C)  1.31cm                                

    D)  2.35 cm

    Correct Answer: D

    Solution :

                     When electron moves at right angles in a magnetic field , then Centripetal force = Force due to magnetic field                 \[\frac{m{{v}^{2}}}{r}=ev\,\,B\sin \theta \] \[\Rightarrow \]               \[r=\frac{m}{e}\,.\,\,\frac{v}{B}\,.\,\,\frac{1}{\sin \theta }\] Given,   \[\frac{e}{m}=1.7\times {{10}^{11}}C/kg\],                 \[v=6\times {{10}^{7}}m/s\],                 \[B=1.5\times {{10}^{-2}}T,\,\,\,\theta ={{90}^{o}}\] \[\Rightarrow \]               \[r=\frac{1}{1.7\times {{10}^{11}}}\times \frac{6\times {{10}^{7}}}{1.5\times {{10}^{-2}}}\]                 \[=2.35\times {{10}^{-2}}m\] \[\Rightarrow \]               \[r=2.35\,\,cm\]


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