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Question

An electron and a proton enter a magnetic field perpendicularly, both have same kinetic energy. Which of the following statements are true?


A
Trajectory of proton is less curved
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B
Trajectory of electron is less curved
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C
Both trajectories are equally curved
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D
Both move on straight line path
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Solution

The correct option is B Trajectory of electron is less curved
When a charged particle enters a magnetic field perpendicularly, it moves on a circular path. The required centripetal force is provided by the magnetic force.
i.e., Magnetic force $$=$$ Centripetal force
$$\Rightarrow qvB=\dfrac { m{ v }^{ 2 } }{ r } $$                ....(i)
Now, kinetic energy of the particle
$$k=\dfrac { 1 }{ 2 } m{ v }^{ 2 }$$
$$\Rightarrow mv=\sqrt { 2mk } $$
Therefore, equation (i) becomes
$$r=\dfrac { \sqrt { 2mk }  }{ qB } \Rightarrow \dfrac { { r }_{ e } }{ { r }_{ p } } =\sqrt { \dfrac { { m }_{ e } }{ { m }_{ p } }  } $$
As, $${ m }_{ e } < { m }_{ p }$$; so, $${ r }_{ e } < { r }_{ p }$$
Hence, trajectory of electron is less curved.

Physics

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