Magnetic Effects & Magnetism

JEE Main level, single correct, medium

140 of 276

Question 140 of 276

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is

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Answer: (B) 2:12:1

Radius of circular path of charged particle (q)\left(q\right) of mass (m)\left(m\right) moving with velocity (v)\left(v\right) in magnetic field (B)\left(B\right) is given by r=mvqBr=\dfrac{mv}{qB}
rαrp=(4m)v(2e)BmveB=2:1\dfrac{{r}_{\alpha }}{{r}_{p}}=\dfrac{\dfrac{\left(4m\right)v}{\left(2e\right)B}}{\dfrac{mv}{eB}}=2:1

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