A) \[1.05\times {{10}^{7}}m/s\]
B) \[5\times {{10}^{6}}m/s\]
C) \[3.2\times {{10}^{3}}m/s\]
D) zero
Correct Answer: A
Solution :
Key Idea: Magnetic force provides- the necessary centripetal force. The magnetic force acting on the electron is \[F=qvB\] ... (i) Centripetal force is \[F=\frac{m{{v}^{2}}}{r}\] ... (ii) Equating Eqs. (i) and (ii), we get \[r=\frac{mv}{eB}\] \[\Rightarrow \] \[v=\frac{eBr}{m}\] Given, \[B=4\times {{10}^{-4}}T,\,e=1.6\times {{10}^{-19}}C\], \[r=0.15\,m,\,m=9.1\times {{10}^{-31}}kg\] \[\therefore \] \[v=\frac{1.6\times {{10}^{-19}}\times 4\times {{10}^{-4}}\times 0.15}{9.1\times {{10}^{-31}}}\] \[v=1.05\times {{10}^{7}}m/s\]
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