A) \[2\pi \sqrt{\frac{{{a}^{2}}}{3G\lambda }}\]
B) \[\pi \sqrt{\frac{{{a}^{2}}}{2G\lambda }}\]
C) \[2\pi \sqrt{\frac{{{a}^{2}}}{2G\lambda }}\]
D) \[2\pi \sqrt{\frac{2{{a}^{2}}}{G\lambda }}\]
Correct Answer: B
Solution :
We know that magnetic force F is always perpendicular to the velocity v of the proton \[\Rightarrow \] \[\mathbf{F}\,.\,\mathbf{v}=0\] or, \[m\mathbf{a}.\mathbf{v}=0\] or, \[\mathbf{a}\,.\,v=0\] \[\Rightarrow \] \[(4\hat{i}+x\hat{j}).\,\,(4\hat{i}+3\hat{j})=0\] or, \[16+0+0+3x=0\] or, \[x=\frac{-16}{3}\]
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