A) \[F\]
B) \[F/2\]
C) \[\sqrt{2}F\]
D) \[2F\]
Correct Answer: C
Solution :
The force due to magnetic field B, acting on electron e moving with velocity v is \[F=e\,v\,B\] ... (i) Also, kinetic energy = energy due to potential V i.e., \[\frac{1}{2}m{{v}^{2}}=eV\] \[\Rightarrow \] \[v={{\left( \frac{2\,eV}{m} \right)}^{1/2}}\] ?.. (ii) From Eqs. (i) and (ii), we get \[F=e\,B{{\left( \frac{2\,eV}{m} \right)}^{1/2}}\] Given, \[{{F}_{1}}=F,\,{{V}_{1}}=V,\,{{V}_{2}}=2\,V\] \[\therefore \] \[\frac{{{F}_{2}}}{{{F}_{1}}}=\frac{\sqrt{{{V}_{2}}}}{{{V}_{1}}}\] \[\Rightarrow \] \[{{F}_{2}}=\frac{\sqrt{2\,V}}{\sqrt{V}}F\] \[\Rightarrow \] \[{{F}_{2}}=\sqrt{2\,}F\]
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