A) \[8\times {{10}^{-12}}N\]
B) \[4\times {{10}^{-12}}N\]
C) \[6\times {{10}^{-12}}N\]
D) none of these
Correct Answer: A
Solution :
Magnetic force on proton is given by \[{{F}_{m}}=q\upsilon B\,\,\sin \theta \]...(i) (Here, \[q=e=1.6\times {{10}^{-19}}C,B=2.5\] tesla) The kinetic energy of proton is \[\frac{1}{2}{{m}_{p}}{{\upsilon }^{2}}=2MeV\] \[=2\times {{10}^{6}}\times 1.6\times {{10}^{-19}}J\] So, \[\upsilon =\frac{\sqrt{2\times 2\times {{10}^{6}}\times 1.6kt{{10}^{-19}}}}{1.6\times {{10}^{-27}}}\] \[=2\times {{10}^{7}}m/s\] Now, from equation (i) we get \[{{F}_{m}}=1.6\times {{10}^{-19}}\times 2\times {{10}^{7}}\times 2.5\sin {{90}^{o}}\] \[=8\times {{10}^{-12}}N\]
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