A) \[~2400\text{ }Vc{{m}^{-1}}\]
B) \[600\text{ }Vc{{m}^{-1}}\]
C) \[~1200\,Vc{{m}^{-1}}\]
D) \[~12000\text{ }V\,c{{m}^{-1}}\]
Correct Answer: C
Solution :
Cathode rays are composed of electrons, when they move in electric field a force \[F=eE\] ?(i) Its acts on them and provides the necessary centripetal force the particles \[F=\frac{m{{v}^{2}}}{r}\] ?(ii) From Eqs. (i) and (ii) we get \[eE=\frac{m{{v}^{2}}}{r}\] \[r=\frac{m{{v}^{2}}}{eE}=\frac{m{{({{10}^{6}})}^{2}}}{e(300)}\] ?(iii) when, velocity is doubled same circular path is followed. Hence, radius is same \[r=\frac{m{{(2\times {{10}^{6}})}^{2}}}{eE}\] ?(iv) Equating Eqs. (iii) and (iv) we get \[\frac{m\times {{({{10}^{6}})}^{2}}}{e(300)}=\frac{m\times {{(2\times {{10}^{6}})}^{2}}}{eE}\] \[E=300\times 4=1200\,V/cm\]
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