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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
    Cathode ray of velocity\[{{10}^{6}}m/s\]describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be

    A)  2400 V/cm                         

    B)  600 V/cm

    C)  1200 V/cm                         

    D)  12000 V/cm

    Correct Answer: C

    Solution :

                    Cathode ray are composed of electrons, \[F=eE\] \[\Rightarrow \]               \[F=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \]               \[eE=\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \]               \[r=\frac{m{{v}^{2}}}{eE}=\frac{m{{({{10}^{6}})}^{2}}}{e(300)}\] When velocity is doubled same circular path is followed hence radius is same                 \[r=\frac{m{{(2\times {{10}^{6}})}^{2}}}{eE}\]                 \[\frac{m\times {{({{10}^{6}})}^{2}}}{300}=\frac{m\times {{(2\times {{10}^{6}})}^{2}}}{eE}\]                 \[E=300\times 4=1200\,V/cm\]


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