An electron and a proton enters into a region of uniform magnetic field at right angles to the field with the same kinetic energy. They describe circular paths of radius $r_{e}$ and $r_{p}$ respectively. then-

r_{e} = r_{p}

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r_{e} < r_{p}

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r_{e} > r_{p}

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r_{e}

may be less than or greater than

r_{p}

depending on the direction of the magnetic field

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Solution

The correct option is B $r_{e} < r_{p}$
Radius of the circular path followed by the charge particles in the magnetic field is,

$r = \frac{m v}{q B} = \frac{P}{q B} = \frac{\sqrt{2 m E_{k}}}{q B}$

Since, $K E$ of the particles is same.

$\Rightarrow r \propto \frac{\sqrt{m}}{q}$

As $q_{e} = q_{p} = e$ and $m_{p} > m_{e}$

$\Rightarrow r_{p} > r_{e}$

 Hence, $(B)$ is the correct answer.

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