A) \[0.81\times {{10}^{-7}}\]
B) \[1.62\times {{10}^{-7}}\]
C) \[2.43\times {{10}^{-7}}\]
D) \[3.24\times {{10}^{-7}}\]
Correct Answer: B
Solution :
When proton enters in a uniform magnetic field at right angle then it moves on a circular path. In this case velocity of proton. \[v=\frac{Bqr}{m}\] where r = radius of circular path Distance covered by proton to traverse 90° arc\[=\frac{1}{4}\]circumference \[d=\frac{1}{4}\times 2\pi r=\pi r/2\] Time taken by proton to cover distance d \[t=\frac{\pi r/2}{v}=\frac{\pi r}{2v}\] \[t=\frac{\pi }{2}\frac{r}{Bqr/m}\] \[t=\frac{\pi m}{2Bq}\] Putting \[m=1.65\times {{10}^{-27}}kg,\] \[B=100mT=100\times {{10}^{-3}}T,q=1.6\times {{10}^{-19}}C\] \[t=\frac{3.14\times 1.65\times {{10}^{-27}}}{2\times 100\times {{10}^{-3}}\times 1.6\times {{10}^{-19}}}\] \[t=1.62\times {{10}^{-7}}\sec \]
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