Magnetic Effects & Magnetism

JEE Main level, numerical answer, medium

137 of 276

Question 137 of 276

A singly ionized magnesium atom (A=24)\left(A=24\right) ion is accelerated to kinetic energy 5keV5keV, and is projected perpendicularly into a magnetic field BB of the magnitude 0.5T0.5T. The radius of path formed will be _____ cm.cm.

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Answer: 10

The radius of circle formed by a charged particle in a magnetic field perpendicular to the velocity is given by,
R=mVqB⇒R=2mKqB=2×24×1.6×10−27×5000×1.6×10−191.6×10−19×0.5=979×10−4m≃10cmR=\dfrac{mV}{qB} \Rightarrow R=\dfrac{\sqrt{2mK}}{qB}=\dfrac{\sqrt{2\times 24\times 1.6\times {10}^{-27}\times 5000\times 1.6\times {10}^{-19}}}{1.6\times {10}^{-19}\times 0.5}=979\times {10}^{-4}m≃10cm

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